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Six 7s: 777777. 1 in 1,000,001

The roll is 777. 1 in 1,000,001

The roll is 0. 1 in 1,000,001

The roll is 1. 1 in 1,000,001

The roll is 2. 1 in 1,000,001

The roll is 3. 1 in 1,000,001

The roll is 4. 1 in 1,000,001

The roll is 5. 1 in 1,000,001

The roll is 6. 1 in 1,000,001

The roll is 7. 1 in 1,000,001

The roll is 8. 1 in 1,000,001

The roll is 9. 1 in 1,000,001

The roll is 69. 1 in 1,000,001

The roll is 696969. 1 in 1,000,001

The roll is 420. 1 in 1,000,001

The roll is 420420. 1 in 1,000,001

The roll is 42. 1 in 1,000,001

The roll is 424242. 1 in 1,000,001

The roll is 666. 1 in 1,000,001

The roll is 666666. 1 in 1,000,001

The roll is 1337. 1 in 1,000,001

The roll is 7734. 1 in 1,000,001

The roll is 80085. 1 in 1,000,001

The roll is 911. 1 in 1,000,001

The roll is 911911. 1 in 1,000,001

The roll is 404. 1 in 1,000,001

The roll is 67. 1 in 1,000,001

The roll is 676767. 1 in 1,000,001

The roll is 86. 1 in 1,000,001

The roll is 101. 1 in 1,000,001

The roll is 365. 1 in 1,000,001

The roll is 365365. 1 in 1,000,001

The roll is 1984. 1 in 1,000,001

The roll is 17776. 1 in 1,000,001

The roll is 86400, the seconds in one day. 1 in 1,000,001

The very top roll: 1,000,000. 1 in 1,000,001

The roll is 69420 or 42069. 1 in 500,000

The roll is 8008 or 58008. 1 in 500,000

The roll is 247365 or 365247: 24/7, all year. 1 in 500,000

Some whole number to the 13th power. 1 in 333,334

Some whole number to the 17th power. 1 in 333,334

Some whole number to the 19th power. 1 in 333,334

The roll is τ cut short: 6283, 62831 or 628318. 1 in 333,334

The roll is φ cut short: 1618, 16180 or 161803. 1 in 333,334

Some whole number to the 10th power. 1 in 250,000

Some whole number to the 11th power. 1 in 250,000

Cut in four, the pieces count up or down by one, in order. 1 in 250,000

The roll is π cut short: 314, 3141, 31415 or 314159. 1 in 250,000

The roll is e cut short: 271, 2718, 27182 or 271828. 1 in 250,000

Some whole number to the 9th power. 1 in 200,000

Some whole number to the 8th power. 1 in 166,667

A number raised to its own power: 1¹, 2², 3³ … up to 7⁷. 1 in 142,857

1, 7, 49, 343… multiplying by 7 each time. 1 in 125,000

Some whole number to the 7th power. 1 in 125,000

Equal to 1 × 2 × 3 × … up to some whole number. 1 in 111,111

1, 5, 25, 125… multiplying by 5 each time. 1 in 111,111

Six digits in a row counting up or down by one. 1 in 111,111

Has 07734 in it, which reads HELLO on an upside-down calculator. 1 in 111,111

A roll from 0 to 9. 1 in 100,000

Last five digits are 00000. 1 in 100,000

Last five digits are 50000. 1 in 100,000

Last five digits are 99999. 1 in 100,000

Five 0s in a row somewhere. 1 in 100,000

The same digit six times in a row. 1 in 100,000

Some whole number to the 6th power. 1 in 90,909

1, 3, 9, 27… tripling all the way. 1 in 76,923

Some whole number to the 5th power. 1 in 62,500

Has 77777 in it. 1 in 52,632

1, 2, 4, 8, 16… doubling all the way. 1 in 50,000

Contains 56789, the top straight. 1 in 50,000

Has 31415 in it. 1 in 50,000

Has 27182 in it. 1 in 50,000

Has 62831 in it. 1 in 50,000

Has 58008 in it, the upside-down calculator classic. 1 in 50,000

Has 80085 in it, the right-way-up calculator classic. 1 in 50,000

Appears in the sequence 0, 1, 1, 2, 3, 5, 8, 13… where each term is the sum of the two before. 1 in 33,333

Counts up by one from start to finish, like 3456. 1 in 33,333

Some whole number to the 4th power. 1 in 31,250

Counts down by one from start to finish, like 6543. 1 in 28,571

Somewhere inside, four numbers count up or down by one back to back. 1 in 26,316

Cut in four, the pieces are consecutive numbers but out of order. 1 in 22,727

Two or more digits, all the same. 1 in 22,222

Has both 69 and 420 in it. 1 in 16,667

Nothing but 0s and 1s. 1 in 15,385

Contains 02468, 13579, or either one backwards. 1 in 14,493

A roll from 10 to 99. 1 in 11,111

Adding its digits gives the same result as multiplying them. 1 in 10,309

Last four digits are 0000. 1 in 10,000

Last four digits are 5000. 1 in 10,000

Last four digits are 9999. 1 in 10,000

Some whole number cubed. 1 in 9,901

Three or more digits that change by the same amount each step. 1 in 8,621

Cut in three, the pieces count up or down by one, in order. 1 in 5,556

Four 0s in a row somewhere. 1 in 5,525

The same digit five times in a row. 1 in 5,525

Turn it upside down and it still reads the same. 1 in 5,025

Five digits in a row counting up or down by one, like 34567. 1 in 4,545

Has 7777 in it. 1 in 3,571

Has 6969 in it. 1 in 3,344

Has 4242 in it. 1 in 3,344

Has 6767 in it. 1 in 3,344

Has 3141 in it. 1 in 3,333

Has 2718 in it. 1 in 3,333

Has 6283 in it. 1 in 3,333

Has 1337 in it. 1 in 3,333

Has 7734 in it, which reads HELL on an upside-down calculator. 1 in 3,333

Has 8008 in it, a calculator classic. 1 in 3,333

Has 1984 in it. 1 in 3,333

Cut in three, the pieces are consecutive numbers but out of order. 1 in 2,778

Two digits taking turns, never the same one twice in a row. 1 in 2,469

Each digit is bigger than the one before. 1 in 2,193

Cut into three or more numbers that grow or shrink by the same ratio. 1 in 2,083

Some digit appears five or more times. 1 in 1,980

Somewhere inside, three numbers count up or down by one back to back. 1 in 1,580

Three different doubled digits back to back, like 113355. 1 in 1,543

Four digits: a doubled digit in the middle, with different digits on each end. 1 in 1,372

Five digits: a tripled digit in the middle, with different digits on each end. 1 in 1,372

Six digits: the middle four identical, with different digits on each end. 1 in 1,372

Each digit is smaller than the one before. 1 in 1,195

A roll from 100 to 999. 1 in 1,111

The second half is a copy of the first half. 1 in 1,001

Anything above 999,000. 1 in 1,000

Equal to some whole number times the next one up, like 6 = 2 × 3. 1 in 1,000

Last three digits are 000. 1 in 1,000

Last three digits are 500. 1 in 1,000

Last three digits are 999. 1 in 1,000

Some whole number multiplied by itself. 1 in 999

Three or more digits that move the same distance each step, up or down. 1 in 910

At least four digits: one odd one out, all the rest identical. 1 in 822

Cut in two, the halves are consecutive numbers, like 1213. 1 in 505

Identical read left to right or right to left. 1 in 500

Three 0s in a row somewhere. 1 in 370

The same digit four times in a row. 1 in 370

Neighbouring digits are never more than one apart. 1 in 360

Has 007 in it. 1 in 346

Its digits add up to more than 45. 1 in 333

A block of three or more of one digit right next to a block of two or more of another. 1 in 301

Has 777 in it. 1 in 270

Has 666 in it. 1 in 270

Four digits in a row counting up or down by one. 1 in 259

Has 404 in it. 1 in 251

Has 101 in it, like an intro course. 1 in 251

Has 314 in it. 1 in 250

Has 271 in it. 1 in 250

Has 420 in it. 1 in 250

Has 911 in it. 1 in 250

Has 365 in it, one for every day of the year. 1 in 250

Every digit is 0, 3, 6 or 9. 1 in 244

Sort the digits and they count up by one with no gaps or repeats. 1 in 227

Built from exactly two different digits. 1 in 217

Digits only go up or stay level, rising at least once. 1 in 202

Cut into three or more numbers that go up or down by the same gap (bigger than 1). 1 in 178

Six digits: two different doubled digits in the middle, with different digits on each end. 1 in 152

Digits only go down or stay level, falling at least once. 1 in 126

Opens with a doubled digit and closes with a different doubled digit. 1 in 111

A roll from 1,000 to 9,999. 1 in 111

Three different digits each appear exactly twice. 1 in 103

The opening two digits reappear as the closing two. 1 in 100

The closing two digits are the opening two flipped around. 1 in 100

Last two digits are 00. 1 in 100

Last two digits are 50. 1 in 100

Last two digits are 25. 1 in 100

Last two digits are 75. 1 in 100

Last two digits are 99. 1 in 100

Some digit appears four or more times. 1 in 84

Cut into three numbers a, b, c so that a + b, a − b, a × b or a ÷ b equals c. 1 in 77

Every digit is between 0 and 4. 1 in 64

Digits climb strictly to a single peak, then drop strictly. 1 in 59

A digit skips one place and lands again, three times in a row. 1 in 53

Every digit is between 5 and 9. 1 in 51

Digits drop strictly to a single low point, then climb strictly. 1 in 42

Two different doubled digits back to back, like 3377. 1 in 40

Two digits immediately repeated, like 4545. 1 in 37

Every digit is even, or every digit is odd. 1 in 28

Digits switch between odd and even at every step. 1 in 28

Two 0s side by side somewhere. 1 in 28

The same digit three times in a row. 1 in 28

Its digits add up to less than 15. 1 in 27

Its digits add up to exactly 21. 1 in 25

One digit at least three times plus another at least twice. 1 in 24

Hides a palindrome at least 4 digits long. 1 in 21

Two 1s, and no other digit appears more than once. 1 in 21

Has 69 in it. 1 in 20

Has 42 in it. 1 in 20

Has 67 in it. 1 in 20

Has 86 in it, kitchen slang for "we're out". 1 in 20

An even number of digits, with both halves adding up to the same total. 1 in 20

The same chunk of 2+ digits shows up twice without overlapping. 1 in 19

Three digits in a row counting up or down by one. 1 in 17

Somewhere inside, a number is followed directly by the next or previous number. 1 in 17

Two separate pieces of the roll, with a gap between them, are one apart. 1 in 16

Digits go up, then down, with level stretches allowed but no second climb. 1 in 16

Only 1 and itself divide it evenly. 1 in 13

Built from exactly three different digits. 1 in 13

A positive multiple of 12. 1 in 12

Digits go down, then up, with level stretches allowed but no second drop. 1 in 12

A roll from 10,000 to 99,999. 1 in 11

A positive multiple of 11. 1 in 11

Divides evenly by the sum of its own digits. 1 in 10

Last digit is 0. 1 in 10

Last digit is 5. 1 in 10

Starts and ends with the same digit. 1 in 10

Same digit at both ends, with something different in between. 1 in 10

At least four digits that zigzag up, down, up… with no repeats side by side. 1 in 7

Some digit appears exactly three times. 1 in 7

A positive multiple of 7. 1 in 7

No digit is used twice. 1 in 6

Three or more side-by-side digits that count up by one once sorted. 1 in 6

First and last digits are one apart. 1 in 5

Two different digits each appear at least twice. 1 in 4

Zigzags up and down once you ignore level stretches, with at least four turns’ worth of digits. 1 in 4

A digit skips one place and lands again, exactly twice in that pattern. 1 in 3

Exactly one 0. 1 in 3

Built from exactly four different digits. 1 in 3

Exactly one 1. 1 in 3

Exactly one 2. 1 in 3

Exactly one 3. 1 in 3

Exactly one 4. 1 in 3

Exactly one 5. 1 in 3

Exactly one 6. 1 in 3

Exactly one 7. 1 in 3

Exactly one 8. 1 in 3

Exactly one 9. 1 in 3

Starts with a smaller digit than it ends with. 1 in 3

The same digit twice side by side. 1 in 2

Has a 7 in it. 1 in 2

An even number. 1 in 2

An odd number. 1 in 2

Starts with a bigger digit than it ends with. 1 in 2

Not a single 0 anywhere. 1 in 2

Two side-by-side digits that are one apart. 1 in 2

Some digit appears at least twice. 1 in 2

A roll from 100,000 to 999,999. 1 in 2