Datasets:
messages listlengths 2 2 | task stringclasses 7
values | meta unknown |
|---|---|---|
[
{
"role": "user",
"content": "3407 % 6 = ?"
},
{
"role": "assistant",
"content": "5"
}
] | mod | {
"n": 3407,
"k": 6,
"base": 10
} |
[
{
"role": "user",
"content": "1476 % 3 = ?"
},
{
"role": "assistant",
"content": "0"
}
] | mod | {
"n": 1476,
"k": 3,
"base": 10
} |
[
{
"role": "user",
"content": "What is the remainder when 3709 is divided by 10?"
},
{
"role": "assistant",
"content": "9"
}
] | mod | {
"n": 3709,
"k": 10,
"base": 10
} |
[
{
"role": "user",
"content": "A server log shows an event at 6:00. What hour (24-hour clock) will it be 16 hours later?"
},
{
"role": "assistant",
"content": "6 is position 6 in the 24-hour cycle. Working it out: 6 + 16 = 22. 22 mod 24 = 22. So it lands on 22."
}
] | hour_24 | {
"start_hour": 6,
"offset": 16,
"direction": "after",
"base": 10,
"clock": 24
} |
[
{
"role": "user",
"content": "A seasonal fruit stand is featuring March's produce now. Which month was it 6 months before?"
},
{
"role": "assistant",
"content": "March corresponds to position 2 out of 12 months. 2 - 6 works out to -4. -4 wraps around (mod 12) to 8. Which gives September."
}
] | months | {
"start_month": "March",
"offset": 6,
"direction": "before",
"base": 10
} |
[
{
"role": "user",
"content": "Add 926 and 578."
},
{
"role": "assistant",
"content": "1504"
}
] | addition | {
"a": 926,
"b": 578,
"digits": 3,
"base": 10
} |
[
{
"role": "user",
"content": "What is 8693 mod 3?"
},
{
"role": "assistant",
"content": "2"
}
] | mod | {
"n": 8693,
"k": 3,
"base": 10
} |
[
{
"role": "user",
"content": "A factory shift starts at 6:00. What hour (24-hour clock) will it be 4 hours later?"
},
{
"role": "assistant",
"content": "Counting positions in the 24-hour cycle, 6 is at 6. Working it out: 6 + 4 = 10. 10 mod 24 reduces to 10. So the answer is 10."
}
] | hour_24 | {
"start_hour": 6,
"offset": 4,
"direction": "after",
"base": 10,
"clock": 24
} |
[
{
"role": "user",
"content": "What is the remainder when 8004 is divided by 2?"
},
{
"role": "assistant",
"content": "0"
}
] | mod | {
"n": 8004,
"k": 2,
"base": 10
} |
[
{
"role": "user",
"content": "If it is August now, what month was it 1 months ago?"
},
{
"role": "assistant",
"content": "August is position 7 in the 12-month cycle. That gives 7 - 1 = 6. 6 wraps around (mod 12) to 6. Which gives July."
}
] | months | {
"start_month": "August",
"offset": 1,
"direction": "before",
"base": 10
} |
[
{
"role": "user",
"content": "241 * 559 = ?"
},
{
"role": "assistant",
"content": "134719"
}
] | multiplication | {
"a": 241,
"b": 559,
"digits": 3,
"base": 10
} |
[
{
"role": "user",
"content": "47 x 70"
},
{
"role": "assistant",
"content": "3290"
}
] | multiplication | {
"a": 47,
"b": 70,
"digits": 2,
"base": 10
} |
[
{
"role": "user",
"content": "60 x 12"
},
{
"role": "assistant",
"content": "720"
}
] | multiplication | {
"a": 60,
"b": 12,
"digits": 2,
"base": 10
} |
[
{
"role": "user",
"content": "The library's return calendar currently shows Monday. 6 days before that, what day of the week was it?"
},
{
"role": "assistant",
"content": "Position-wise, Monday is 0 within the 7-day cycle. Computing 0 - 6 yields -6. -6 wraps around (mod 7) to 1. Which means the ... | days_of_week | {
"start_day": "Monday",
"offset": 6,
"direction": "before",
"base": 10
} |
[
{
"role": "user",
"content": "6765 % 5 = ?"
},
{
"role": "assistant",
"content": "0"
}
] | mod | {
"n": 6765,
"k": 5,
"base": 10
} |
[
{
"role": "user",
"content": "What is 916 times 669?"
},
{
"role": "assistant",
"content": "612804"
}
] | multiplication | {
"a": 916,
"b": 669,
"digits": 3,
"base": 10
} |
[
{
"role": "user",
"content": "What is the remainder when 3922 is divided by 7?"
},
{
"role": "assistant",
"content": "2"
}
] | mod | {
"n": 3922,
"k": 7,
"base": 10
} |
[
{
"role": "user",
"content": "A museum's featured exhibit this month is November's theme. 3 months later, what month will it be?"
},
{
"role": "assistant",
"content": "November is position 10 in the 12-month cycle. Computing 10 + 3 yields 13. 13 wraps around (mod 12) to 1. That corresponds to Fe... | months | {
"start_month": "November",
"offset": 3,
"direction": "after",
"base": 10
} |
[
{
"role": "user",
"content": "What is 790 plus 718?"
},
{
"role": "assistant",
"content": "1508"
}
] | addition | {
"a": 790,
"b": 718,
"digits": 3,
"base": 10
} |
[
{
"role": "user",
"content": "Multiply 52 by 65."
},
{
"role": "assistant",
"content": "3380"
}
] | multiplication | {
"a": 52,
"b": 65,
"digits": 2,
"base": 10
} |
[
{
"role": "user",
"content": "What is 13 times 57?"
},
{
"role": "assistant",
"content": "741"
}
] | multiplication | {
"a": 13,
"b": 57,
"digits": 2,
"base": 10
} |
[
{
"role": "user",
"content": "3 months after December is"
},
{
"role": "assistant",
"content": "Counting positions in the 12-month cycle, December is at 11. That gives 11 + 3 = 14. 14 wraps around (mod 12) to 2. So it lands on March."
}
] | months | {
"start_month": "December",
"offset": 3,
"direction": "after",
"base": 10
} |
[
{
"role": "user",
"content": "Priya's flight departs at 1:00. 3 hours later, what hour will it be?"
},
{
"role": "assistant",
"content": "In the 24-hour cycle, 1 sits at position 1. 1 + 3 works out to 4. Reducing 4 mod 24 gives 4. Which means the answer is 4."
}
] | hour_24 | {
"start_hour": 1,
"offset": 3,
"direction": "after",
"base": 10,
"clock": 24
} |
[
{
"role": "user",
"content": "82 * 10 = ?"
},
{
"role": "assistant",
"content": "820"
}
] | multiplication | {
"a": 82,
"b": 10,
"digits": 2,
"base": 10
} |
[
{
"role": "user",
"content": "5728 % 10 = ?"
},
{
"role": "assistant",
"content": "8"
}
] | mod | {
"n": 5728,
"k": 10,
"base": 10
} |
[
{
"role": "user",
"content": "What hour is it 1 hours before 15:00 (24-hour clock)?"
},
{
"role": "assistant",
"content": "15 is position 15 in the 24-hour cycle. That gives 15 - 1 = 14. Reducing 14 mod 24 gives 14. So it lands on 14."
}
] | hour_24 | {
"start_hour": 15,
"offset": 1,
"direction": "before",
"base": 10,
"clock": 24
} |
[
{
"role": "user",
"content": "Omar set an alarm for 4 o'clock. What hour will it be 3 hours later?"
},
{
"role": "assistant",
"content": "4 is position 3 in the 12-hour cycle. Computing 3 + 3 yields 6. Taking 6 mod 12 leaves 6. So it lands on 7."
}
] | hour_12 | {
"start_hour": 4,
"offset": 3,
"direction": "after",
"base": 10,
"clock": 12
} |
[
{
"role": "user",
"content": "A radio station's featured album pick for February is out now. Counting 10 months forward, what month is that?"
},
{
"role": "assistant",
"content": "February corresponds to position 1 out of 12 months. 1 + 10 = 11. 11 mod 12 = 11. Which means the answer is December... | months | {
"start_month": "February",
"offset": 10,
"direction": "after",
"base": 10
} |
[
{
"role": "user",
"content": "A security patrol begins its round at 3:00. 2 hours later, what hour will it be?"
},
{
"role": "assistant",
"content": "Counting positions in the 24-hour cycle, 3 is at 3. 3 + 2 works out to 5. Taking 5 mod 24 leaves 5. That corresponds to 5."
}
] | hour_24 | {
"start_hour": 3,
"offset": 2,
"direction": "after",
"base": 10,
"clock": 24
} |
[
{
"role": "user",
"content": "A puzzle subscription box arrived today, Wednesday. 11 days later, what day of the week will it be?"
},
{
"role": "assistant",
"content": "Wednesday corresponds to position 2 out of 7 days. Computing 2 + 11 yields 13. 13 mod 7 reduces to 6. Which gives Sunday."
}
... | days_of_week | {
"start_day": "Wednesday",
"offset": 11,
"direction": "after",
"base": 10
} |
[
{
"role": "user",
"content": "7118 % 3 = ?"
},
{
"role": "assistant",
"content": "2"
}
] | mod | {
"n": 7118,
"k": 3,
"base": 10
} |
[
{
"role": "user",
"content": "10 months after February is"
},
{
"role": "assistant",
"content": "In the 12-month cycle, February sits at position 1. Computing 1 + 10 yields 11. Taking 11 mod 12 leaves 11. Which gives December."
}
] | months | {
"start_month": "February",
"offset": 10,
"direction": "after",
"base": 10
} |
[
{
"role": "user",
"content": "A cargo ship's watch begins at 14:00. What hour comes up after 18 more hours?"
},
{
"role": "assistant",
"content": "Counting positions in the 24-hour cycle, 14 is at 14. 14 + 18 works out to 32. 32 wraps around (mod 24) to 8. That corresponds to 8."
}
] | hour_24 | {
"start_hour": 14,
"offset": 18,
"direction": "after",
"base": 10,
"clock": 24
} |
[
{
"role": "user",
"content": "A data backup job kicks off at 9:00. Counting 5 hours forward, what hour is that?"
},
{
"role": "assistant",
"content": "Counting positions in the 24-hour cycle, 9 is at 9. Computing 9 + 5 yields 14. 14 mod 24 = 14. So the answer is 14."
}
] | hour_24 | {
"start_hour": 9,
"offset": 5,
"direction": "after",
"base": 10,
"clock": 24
} |
[
{
"role": "user",
"content": "818 x 441"
},
{
"role": "assistant",
"content": "360738"
}
] | multiplication | {
"a": 818,
"b": 441,
"digits": 3,
"base": 10
} |
[
{
"role": "user",
"content": "A security patrol begins its round at 18:00. Counting 18 hours forward, what hour is that?"
},
{
"role": "assistant",
"content": "18 corresponds to position 18 out of 24 hours. 18 + 18 works out to 36. 36 mod 24 reduces to 12. Which means the answer is 12."
}
] | hour_24 | {
"start_hour": 18,
"offset": 18,
"direction": "after",
"base": 10,
"clock": 24
} |
[
{
"role": "user",
"content": "The observatory's current shift began at 7 o'clock. 10 hours before that, what hour was it?"
},
{
"role": "assistant",
"content": "Position-wise, 7 is 6 within the 12-hour cycle. That gives 6 - 10 = -4. -4 mod 12 = 8. Which gives 9."
}
] | hour_12 | {
"start_hour": 7,
"offset": 10,
"direction": "before",
"base": 10,
"clock": 12
} |
[
{
"role": "user",
"content": "What is 459 plus 951?"
},
{
"role": "assistant",
"content": "1410"
}
] | addition | {
"a": 459,
"b": 951,
"digits": 3,
"base": 10
} |
[
{
"role": "user",
"content": "20 x 48"
},
{
"role": "assistant",
"content": "960"
}
] | multiplication | {
"a": 20,
"b": 48,
"digits": 2,
"base": 10
} |
[
{
"role": "user",
"content": "A parking meter was just set at 1 o'clock. What hour comes up after 8 more hours?"
},
{
"role": "assistant",
"content": "Position-wise, 1 is 0 within the 12-hour cycle. Working it out: 0 + 8 = 8. Reducing 8 mod 12 gives 8. So the answer is 9."
}
] | hour_12 | {
"start_hour": 1,
"offset": 8,
"direction": "after",
"base": 10,
"clock": 12
} |
[
{
"role": "user",
"content": "13 hours before 2:00 is"
},
{
"role": "assistant",
"content": "Position-wise, 2 is 2 within the 24-hour cycle. Working it out: 2 - 13 = -11. -11 wraps around (mod 24) to 13. So the answer is 13."
}
] | hour_24 | {
"start_hour": 2,
"offset": 13,
"direction": "before",
"base": 10,
"clock": 24
} |
[
{
"role": "user",
"content": "93 * 41 = ?"
},
{
"role": "assistant",
"content": "3813"
}
] | multiplication | {
"a": 93,
"b": 41,
"digits": 2,
"base": 10
} |
[
{
"role": "user",
"content": "Multiply 392 by 685."
},
{
"role": "assistant",
"content": "268520"
}
] | multiplication | {
"a": 392,
"b": 685,
"digits": 3,
"base": 10
} |
[
{
"role": "user",
"content": "What is 5167 plus 4404?"
},
{
"role": "assistant",
"content": "9571"
}
] | addition | {
"a": 5167,
"b": 4404,
"digits": 4,
"base": 10
} |
[
{
"role": "user",
"content": "What is 550 plus 139?"
},
{
"role": "assistant",
"content": "689"
}
] | addition | {
"a": 550,
"b": 139,
"digits": 3,
"base": 10
} |
[
{
"role": "user",
"content": "A server log shows an event at 13:00. Counting 6 hours back, what hour was that?"
},
{
"role": "assistant",
"content": "13 corresponds to position 13 out of 24 hours. Working it out: 13 - 6 = 7. Reducing 7 mod 24 gives 7. That corresponds to 7."
}
] | hour_24 | {
"start_hour": 13,
"offset": 6,
"direction": "before",
"base": 10,
"clock": 24
} |
[
{
"role": "user",
"content": "A magazine's current cover story is themed around March. Counting 14 months back, what month was that?"
},
{
"role": "assistant",
"content": "Position-wise, March is 2 within the 12-month cycle. Computing 2 - 14 yields -12. Taking -12 mod 12 leaves 0. So it lands on... | months | {
"start_month": "March",
"offset": 14,
"direction": "before",
"base": 10
} |
[
{
"role": "user",
"content": "3523 + 9129 = ?"
},
{
"role": "assistant",
"content": "12652"
}
] | addition | {
"a": 3523,
"b": 9129,
"digits": 4,
"base": 10
} |
[
{
"role": "user",
"content": "491 % 6 = ?"
},
{
"role": "assistant",
"content": "5"
}
] | mod | {
"n": 491,
"k": 6,
"base": 10
} |
[
{
"role": "user",
"content": "A community garden's current planting guide is for May. What month was it 1 months earlier?"
},
{
"role": "assistant",
"content": "May is position 4 in the 12-month cycle. Working it out: 4 - 1 = 3. 3 wraps around (mod 12) to 3. Which gives April."
}
] | months | {
"start_month": "May",
"offset": 1,
"direction": "before",
"base": 10
} |
[
{
"role": "user",
"content": "What is 3377 plus 4397?"
},
{
"role": "assistant",
"content": "7774"
}
] | addition | {
"a": 3377,
"b": 4397,
"digits": 4,
"base": 10
} |
[
{
"role": "user",
"content": "Carlos's trivia night meets today, Saturday. What day of the week will it be 1 days from now?"
},
{
"role": "assistant",
"content": "Saturday is position 5 in the 7-day cycle. Working it out: 5 + 1 = 6. 6 wraps around (mod 7) to 6. So it lands on Sunday."
}
] | days_of_week | {
"start_day": "Saturday",
"offset": 1,
"direction": "after",
"base": 10
} |
[
{
"role": "user",
"content": "What is 2050 mod 2?"
},
{
"role": "assistant",
"content": "0"
}
] | mod | {
"n": 2050,
"k": 2,
"base": 10
} |
[
{
"role": "user",
"content": "Multiply 95 by 10."
},
{
"role": "assistant",
"content": "950"
}
] | multiplication | {
"a": 95,
"b": 10,
"digits": 2,
"base": 10
} |
[
{
"role": "user",
"content": "A data backup job finished at 12:00. 5 hours before that, what hour was it?"
},
{
"role": "assistant",
"content": "In the 24-hour cycle, 12 sits at position 12. Computing 12 - 5 yields 7. 7 mod 24 reduces to 7. That corresponds to 7."
}
] | hour_24 | {
"start_hour": 12,
"offset": 5,
"direction": "before",
"base": 10,
"clock": 24
} |
[
{
"role": "user",
"content": "Multiply 67 by 89."
},
{
"role": "assistant",
"content": "5963"
}
] | multiplication | {
"a": 67,
"b": 89,
"digits": 2,
"base": 10
} |
[
{
"role": "user",
"content": "What is 7120 mod 6?"
},
{
"role": "assistant",
"content": "4"
}
] | mod | {
"n": 7120,
"k": 6,
"base": 10
} |
[
{
"role": "user",
"content": "A data backup job finished at 10:00. What hour was it 2 hours earlier?"
},
{
"role": "assistant",
"content": "Counting positions in the 24-hour cycle, 10 is at 10. 10 - 2 works out to 8. 8 wraps around (mod 24) to 8. So the answer is 8."
}
] | hour_24 | {
"start_hour": 10,
"offset": 2,
"direction": "before",
"base": 10,
"clock": 24
} |
[
{
"role": "user",
"content": "Elena started studying at 12 o'clock. What hour comes up after 7 more hours?"
},
{
"role": "assistant",
"content": "Position-wise, 12 is 11 within the 12-hour cycle. 11 + 7 = 18. 18 mod 12 reduces to 6. Which means the answer is 7."
}
] | hour_12 | {
"start_hour": 12,
"offset": 7,
"direction": "after",
"base": 10,
"clock": 12
} |
[
{
"role": "user",
"content": "3796 % 2 = ?"
},
{
"role": "assistant",
"content": "0"
}
] | mod | {
"n": 3796,
"k": 2,
"base": 10
} |
[
{
"role": "user",
"content": "What is 867 times 505?"
},
{
"role": "assistant",
"content": "437835"
}
] | multiplication | {
"a": 867,
"b": 505,
"digits": 3,
"base": 10
} |
[
{
"role": "user",
"content": "What hour is it 11 hours before 9 o'clock?"
},
{
"role": "assistant",
"content": "In the 12-hour cycle, 9 sits at position 8. Computing 8 - 11 yields -3. -3 wraps around (mod 12) to 9. Which gives 10."
}
] | hour_12 | {
"start_hour": 9,
"offset": 11,
"direction": "before",
"base": 10,
"clock": 12
} |
[
{
"role": "user",
"content": "A coffee shop's specialty drink for November just launched. 4 months later, what month will it be?"
},
{
"role": "assistant",
"content": "November corresponds to position 10 out of 12 months. Computing 10 + 4 yields 14. 14 mod 12 reduces to 2. Which means the answer... | months | {
"start_month": "November",
"offset": 4,
"direction": "after",
"base": 10
} |
[
{
"role": "user",
"content": "Multiply 688 by 769."
},
{
"role": "assistant",
"content": "529072"
}
] | multiplication | {
"a": 688,
"b": 769,
"digits": 3,
"base": 10
} |
[
{
"role": "user",
"content": "A puzzle subscription box arrived on Thursday. Which day was it 1 days before?"
},
{
"role": "assistant",
"content": "Counting positions in the 7-day cycle, Thursday is at 3. Working it out: 3 - 1 = 2. Taking 2 mod 7 leaves 2. Which gives Wednesday."
}
] | days_of_week | {
"start_day": "Thursday",
"offset": 1,
"direction": "before",
"base": 10
} |
[
{
"role": "user",
"content": "What is 2848 plus 4403?"
},
{
"role": "assistant",
"content": "7251"
}
] | addition | {
"a": 2848,
"b": 4403,
"digits": 4,
"base": 10
} |
[
{
"role": "user",
"content": "900 + 683"
},
{
"role": "assistant",
"content": "1583"
}
] | addition | {
"a": 900,
"b": 683,
"digits": 3,
"base": 10
} |
[
{
"role": "user",
"content": "Yuki checked their watch: 9 o'clock. Counting 13 hours back, what hour was that?"
},
{
"role": "assistant",
"content": "In the 12-hour cycle, 9 sits at position 8. That gives 8 - 13 = -5. -5 mod 12 = 7. So it lands on 8."
}
] | hour_12 | {
"start_hour": 9,
"offset": 13,
"direction": "before",
"base": 10,
"clock": 12
} |
[
{
"role": "user",
"content": "A puzzle subscription box arrived on Saturday. 19 days before that, what day of the week was it?"
},
{
"role": "assistant",
"content": "Saturday corresponds to position 5 out of 7 days. That gives 5 - 19 = -14. -14 wraps around (mod 7) to 0. Which gives Monday."
}... | days_of_week | {
"start_day": "Saturday",
"offset": 19,
"direction": "before",
"base": 10
} |
[
{
"role": "user",
"content": "What month is 10 months before June?"
},
{
"role": "assistant",
"content": "Counting positions in the 12-month cycle, June is at 5. 5 - 10 works out to -5. -5 mod 12 reduces to 7. That corresponds to August."
}
] | months | {
"start_month": "June",
"offset": 10,
"direction": "before",
"base": 10
} |
[
{
"role": "user",
"content": "Add 8706 and 2387."
},
{
"role": "assistant",
"content": "11093"
}
] | addition | {
"a": 8706,
"b": 2387,
"digits": 4,
"base": 10
} |
[
{
"role": "user",
"content": "1218 % 2 = ?"
},
{
"role": "assistant",
"content": "0"
}
] | mod | {
"n": 1218,
"k": 2,
"base": 10
} |
[
{
"role": "user",
"content": "A puzzle subscription box arrived on Sunday. What day of the week was it 18 days earlier?"
},
{
"role": "assistant",
"content": "Counting positions in the 7-day cycle, Sunday is at 6. 6 - 18 works out to -12. Taking -12 mod 7 leaves 2. So the answer is Wednesday."
... | days_of_week | {
"start_day": "Sunday",
"offset": 18,
"direction": "before",
"base": 10
} |
[
{
"role": "user",
"content": "A radio station's featured album pick for June is out now. 13 months later, what month will it be?"
},
{
"role": "assistant",
"content": "Counting positions in the 12-month cycle, June is at 5. That gives 5 + 13 = 18. 18 mod 12 reduces to 6. Which gives July."
}
] | months | {
"start_month": "June",
"offset": 13,
"direction": "after",
"base": 10
} |
[
{
"role": "user",
"content": "A cargo ship's watch begins at 19:00. Counting 9 hours forward, what hour is that?"
},
{
"role": "assistant",
"content": "Position-wise, 19 is 19 within the 24-hour cycle. That gives 19 + 9 = 28. 28 wraps around (mod 24) to 4. Which gives 4."
}
] | hour_24 | {
"start_hour": 19,
"offset": 9,
"direction": "after",
"base": 10,
"clock": 24
} |
[
{
"role": "user",
"content": "Multiply 359 by 268."
},
{
"role": "assistant",
"content": "96212"
}
] | multiplication | {
"a": 359,
"b": 268,
"digits": 3,
"base": 10
} |
[
{
"role": "user",
"content": "A community garden's current planting guide is for June. Which month was it 10 months before?"
},
{
"role": "assistant",
"content": "June is position 5 in the 12-month cycle. Working it out: 5 - 10 = -5. -5 mod 12 reduces to 7. Which gives August."
}
] | months | {
"start_month": "June",
"offset": 10,
"direction": "before",
"base": 10
} |
[
{
"role": "user",
"content": "Add 3863 and 6534."
},
{
"role": "assistant",
"content": "10397"
}
] | addition | {
"a": 3863,
"b": 6534,
"digits": 4,
"base": 10
} |
[
{
"role": "user",
"content": "What is 7479 mod 3?"
},
{
"role": "assistant",
"content": "0"
}
] | mod | {
"n": 7479,
"k": 3,
"base": 10
} |
[
{
"role": "user",
"content": "7170 + 8645 = ?"
},
{
"role": "assistant",
"content": "15815"
}
] | addition | {
"a": 7170,
"b": 8645,
"digits": 4,
"base": 10
} |
[
{
"role": "user",
"content": "8814 % 7 = ?"
},
{
"role": "assistant",
"content": "1"
}
] | mod | {
"n": 8814,
"k": 7,
"base": 10
} |
[
{
"role": "user",
"content": "270 + 574 = ?"
},
{
"role": "assistant",
"content": "844"
}
] | addition | {
"a": 270,
"b": 574,
"digits": 3,
"base": 10
} |
[
{
"role": "user",
"content": "5508 + 4390"
},
{
"role": "assistant",
"content": "9898"
}
] | addition | {
"a": 5508,
"b": 4390,
"digits": 4,
"base": 10
} |
[
{
"role": "user",
"content": "61 + 54 = ?"
},
{
"role": "assistant",
"content": "115"
}
] | addition | {
"a": 61,
"b": 54,
"digits": 2,
"base": 10
} |
[
{
"role": "user",
"content": "A bakery's oven now reads 6 o'clock. Which hour was it 8 hours before?"
},
{
"role": "assistant",
"content": "In the 12-hour cycle, 6 sits at position 5. Computing 5 - 8 yields -3. Reducing -3 mod 12 gives 9. Which gives 10."
}
] | hour_12 | {
"start_hour": 6,
"offset": 8,
"direction": "before",
"base": 10,
"clock": 12
} |
[
{
"role": "user",
"content": "436 x 911"
},
{
"role": "assistant",
"content": "397196"
}
] | multiplication | {
"a": 436,
"b": 911,
"digits": 3,
"base": 10
} |
[
{
"role": "user",
"content": "396 + 863 = ?"
},
{
"role": "assistant",
"content": "1259"
}
] | addition | {
"a": 396,
"b": 863,
"digits": 3,
"base": 10
} |
[
{
"role": "user",
"content": "Carlos's meeting ends at 19:00. What hour was it 5 hours earlier?"
},
{
"role": "assistant",
"content": "In the 24-hour cycle, 19 sits at position 19. Working it out: 19 - 5 = 14. Reducing 14 mod 24 gives 14. That corresponds to 14."
}
] | hour_24 | {
"start_hour": 19,
"offset": 5,
"direction": "before",
"base": 10,
"clock": 24
} |
[
{
"role": "user",
"content": "What is 819 mod 10?"
},
{
"role": "assistant",
"content": "9"
}
] | mod | {
"n": 819,
"k": 10,
"base": 10
} |
[
{
"role": "user",
"content": "Add 633 and 509."
},
{
"role": "assistant",
"content": "1142"
}
] | addition | {
"a": 633,
"b": 509,
"digits": 3,
"base": 10
} |
[
{
"role": "user",
"content": "7 months before November is"
},
{
"role": "assistant",
"content": "Counting positions in the 12-month cycle, November is at 10. Working it out: 10 - 7 = 3. 3 mod 12 reduces to 3. So the answer is April."
}
] | months | {
"start_month": "November",
"offset": 7,
"direction": "before",
"base": 10
} |
[
{
"role": "user",
"content": "What is the remainder when 1065 is divided by 7?"
},
{
"role": "assistant",
"content": "1"
}
] | mod | {
"n": 1065,
"k": 7,
"base": 10
} |
[
{
"role": "user",
"content": "Yuki's train arrives at 3 o'clock. Counting 6 hours back, what hour was that?"
},
{
"role": "assistant",
"content": "Position-wise, 3 is 2 within the 12-hour cycle. Computing 2 - 6 yields -4. Taking -4 mod 12 leaves 8. So it lands on 9."
}
] | hour_12 | {
"start_hour": 3,
"offset": 6,
"direction": "before",
"base": 10,
"clock": 12
} |
[
{
"role": "user",
"content": "A vending machine was last restocked at 2 o'clock. Counting 10 hours back, what hour was that?"
},
{
"role": "assistant",
"content": "Counting positions in the 12-hour cycle, 2 is at 1. That gives 1 - 10 = -9. -9 mod 12 reduces to 3. So the answer is 4."
}
] | hour_12 | {
"start_hour": 2,
"offset": 10,
"direction": "before",
"base": 10,
"clock": 12
} |
[
{
"role": "user",
"content": "12 * 89 = ?"
},
{
"role": "assistant",
"content": "1068"
}
] | multiplication | {
"a": 12,
"b": 89,
"digits": 2,
"base": 10
} |
[
{
"role": "user",
"content": "If the clock shows 6 o'clock, what will it show in 4 hours?"
},
{
"role": "assistant",
"content": "6 corresponds to position 5 out of 12 hours. 5 + 4 = 9. 9 mod 12 reduces to 9. Which means the answer is 10."
}
] | hour_12 | {
"start_hour": 6,
"offset": 4,
"direction": "after",
"base": 10,
"clock": 12
} |
[
{
"role": "user",
"content": "What is 69 times 10?"
},
{
"role": "assistant",
"content": "690"
}
] | multiplication | {
"a": 69,
"b": 10,
"digits": 2,
"base": 10
} |
[
{
"role": "user",
"content": "What is 3136 mod 5?"
},
{
"role": "assistant",
"content": "1"
}
] | mod | {
"n": 3136,
"k": 5,
"base": 10
} |
[
{
"role": "user",
"content": "What is 3297 mod 10?"
},
{
"role": "assistant",
"content": "7"
}
] | mod | {
"n": 3297,
"k": 10,
"base": 10
} |
[
{
"role": "user",
"content": "A factory shift starts at 22:00. 3 hours later, what hour will it be?"
},
{
"role": "assistant",
"content": "Position-wise, 22 is 22 within the 24-hour cycle. 22 + 3 = 25. Reducing 25 mod 24 gives 1. So the answer is 1."
}
] | hour_24 | {
"start_hour": 22,
"offset": 3,
"direction": "after",
"base": 10,
"clock": 24
} |
End of preview. Expand in Data Studio
Math + Cyclic-Time Synthetic Dataset
Synthetic dataset for training a small (~10M-100M param), task-specialized LLM on arithmetic (addition, multiplication), cyclic time arithmetic (days-of-week, months, 12-hour and 24-hour clock), and mod-k remainder probes — generalization-focused rather than memorization, following on from the T2/T5/T10 modular-circuit discussion. Days-of-week, months, and hours are all instances of the same underlying cyclic/modular-addition structure, rendered as different surface forms.
Generate
python3 generate_math_dataset.py --out data_base10
Key flags: --base (numeral base for rendering numbers, default 10 — use
--base 6 or --base 7 to produce transfer-experiment variants of the same
task distribution once a base-10 model is working), --seed, plus per-task
length/range/count knobs (--add-train-lengths, --mod-n-per-modulus, etc.
— see --help).
Cyclic tasks: story-wrapping + worked-reasoning traces
The four cyclic tasks (days_of_week, months, hour_12, hour_24) are
built differently from the arithmetic/mod tasks, to address a specific
failure mode: a 100M-param model has no way to compute (start - offset) mod cycle_len correctly in a single forward pass if the assistant turn is just
the bare answer — it has no token positions to actually do the subtraction
and mod-reduction, so it tends to fall back to surface pattern-matching
("if the question mentions months, just output a month") instead of learning
the circuit.
To address this:
- Worked-reasoning trace, composed not templated: the assistant turn
spells out the computation via 4 independently-varying phrase pools —
opener / operation / mod-reduce / conclusion — combined at random (4^4 =
256 wordings), e.g.
"Position-wise, Saturday is 5 within the 7-day cycle. That gives 5 + 10 = 15. Taking 15 mod 7 leaves 1. That corresponds to Tuesday."vs"Thursday corresponds to position 3 out of 7 days. 3 - 13 = -10. -10 mod 7 = 4. So it lands on Friday."Every conclusion variant ends in"... {label}."with the label as the last word, so verification stays format-agnostic regardless of which wording was drawn. This is a deliberate design choice, not an accident: the computation structure (position → op → mod-reduce → label) stays identical every time — that consistency is what lets a small model actually learn the algorithm — only the wording around it varies, both so the raw-text corpus doesn't read as one stamped-out template, and to stop the model from overfitting to one exact reasoning string. - Story-wrapped questions, composed not templated: ~70% of cyclic examples combine a random scenario setup (museum exhibit rotations, bakery oven timers, flight schedules, library due dates, factory shift changes, etc. — 8 per task/direction) with a random tail question (4 per task/direction), giving 32 surface forms per task/direction instead of a handful of fixed full-sentence templates. The remaining ~30% use the original plain templates.
- Offsets weighted toward small values: only a handful of simple
"N months/hours/days" question shapes exist, so uniformly sampling any
offset gives too few unique (start, offset, direction) facts to be rich
data — and repetitive large-offset drills ("604 months ago, again and
again") aren't useful training data anyway. Train offsets are drawn mostly
from 1-12 (75% of the time,
--cyclic-small-frac) with a thin tail up to 20 (--cyclic-tail-hi); each unique fact is paraphrased up to--cyclic-repeat-cap(default 10) times with different question/reasoning compositions to fill out the requested count without inventing new underlying facts.test_oodpushes offsets well past that — a near zone (21-60) and a smaller far zone (61-600,--cyclic-ood-far-frac) that specifically tests far/multi-cycle extrapolation, never seen in train.
Arithmetic (addition, multiplication) and mod tasks are unchanged this
round — bare numeric answers, no reasoning trace yet.
Splits
train.jsonl— in-distribution training examples.test_id.jsonl— held-out in-distribution examples (same digit-length / offset / value range as train, but the exact input was never trained on). Deterministic hash-based split (stable_bucket), ~5% of in-range examples, reproducible across runs regardless ofPYTHONHASHSEED.test_ood.jsonl— out-of-distribution examples: longer digit lengths for addition/multiplication, larger offsets for days-of-week, and larger values for mod probes than anything seen in train. Tests whether the model learned the underlying algorithm/circuit vs. memorized surface patterns.
Schema
Each line is a JSON object:
{
"messages": [
{"role": "user", "content": "127 + 489 = ?"},
{"role": "assistant", "content": "616"}
],
"task": "addition",
"meta": {"a": 127, "b": 489, "digits": 3, "base": 10}
}
Cyclic-task assistant turns are a worked-reasoning trace ending in the label, not a bare answer:
{
"messages": [
{"role": "user", "content": "If it is July now, what month will it be in 3 months?"},
{"role": "assistant", "content": "July is position 6 in the 12-month cycle. 6 + 3 = 9, and 9 mod 12 = 9, so the answer is October."}
],
"task": "months",
"meta": {"start_month": "July", "offset": 3, "direction": "after", "base": 10}
}
task is one of addition, multiplication, days_of_week, months,
hour_12, hour_24, mod. meta carries the ground-truth operands so
correctness/leakage can be re-verified without re-parsing the text. All
numbers in the messages text are rendered in the same --base —
including the modulus, day/month offset, and hour — so a --base 6 run is
self-consistent throughout. hour_12 cycles through 1..12 (clock-style, no
zero); hour_24 cycles through 0..23.
Arithmetic/mod tasks have 3-4 paraphrase templates. Cyclic tasks draw from a mix of 3 plain templates + 5 story-scenario templates per direction (see above) so the model isn't just pattern-matching one surface form.
train_raw.txt is a flattened, role-marker-free version of train.jsonl
({user question} {assistant answer/reasoning} per line, blank-line
separated) for pretraining-style corpora — flatten format/separator can be
adjusted once nanochat's data-loader format is confirmed.
Dataset stats
data_base10 (--base 10, composed story-wrapped + reasoning-trace cyclic tasks):
train: 50061 addition 11490, multiplication 7708, mod 11437, days_of_week 2322, months 4292, hour_12 4227, hour_24 8585
test_id: 2639 addition 610, multiplication 392, mod 563, days_of_week 178, months 208, hour_12 273, hour_24 415
test_ood: 7800 addition 1000, multiplication 1000, mod 1800, days_of_week 1000, months 1000, hour_12 1000, hour_24 1000
train_raw: 50061 lines (flattened, no role markers)
Cyclic-task train counts are lower than the arithmetic tasks because the
small-offset weighting (mostly 1-12, tail to 20) only produces a few hundred
to ~1000 unique underlying facts per task (cycle_len × offset_range × 2 directions); each is paraphrased up to --cyclic-repeat-cap (10) times
to fill out the count — not an error, a deliberate small/rich-phrasing
tradeoff per the plan above.
Verified: 0 numeric/cyclic-label mismatches across all 60,500 chat examples
(reasoning-trace math re-derived independently from meta and compared),
and zero (task, operands) overlap between train/test_id/test_ood (32,706 /
1,694 / 7,800 unique facts respectively).
data_base6/ and data_base7/ (pushed earlier, transfer-experiment
variants) still use the old plain-template/bare-answer schema for
months/hours — not yet regenerated with story-wrapping + reasoning traces.
Base-10 is the priority baseline for now; base-6/7 will be refreshed once a
base-10 model is trained and working.
Not yet done
- base-6/base-7 story+reasoning refresh (see above).
- Reasoning traces for addition/multiplication/mod (currently bare answers only) — same "can't compute in one forward pass" argument likely applies to multi-digit arithmetic too, just out of scope for this iteration.
train_raw.txtseparator/format not yet confirmed against nanochat's actual data loader.
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