Rarebit badges: all 53, with exact odds
Counts come from scoring every number from 0 to 999,999. Rarer badges earn more points: a badge half as common is worth 10 more. Only the best badge in each family counts toward a score. The exact formula is on how it works.
In the exact rules, n is the number, s is its digits written out, and L is how many digits it has.
Digits 12 badges
| Badge | What it means | Example | Count | Odds | Points |
|---|---|---|---|---|---|
| Solid Block | Every digit is the same, like 4444 Exact rule: L ≥ 2 and every digit is the same (e.g. 4444) | 11 | 45 | 1 in 22,222 | 144 |
| Double Take | The same digit twice in a row, like 4,778 Exact rule: s contains a run of the same digit of length ≥ 2 | 11 | 402,129 | about 1 in 2.5 | 13 |
| Triple Stack | The same digit three times in a row, like 52,229 Exact rule: s contains a run of the same digit of length ≥ 3 | 111 | 35,919 | 1 in 28 | 48 |
| Tower of Four | The same digit four times in a row, like 18,888 Exact rule: s contains a run of the same digit of length ≥ 4 | 1,111 | 2,700 | 1 in 370 | 85 |
| Tower of Five | The same digit five times in a row, like 333,337 Exact rule: s contains a run of the same digit of length ≥ 5 | 11,111 | 180 | 1 in 5,556 | 124 |
| Mirror Image | Reads the same forwards and backwards, like 12,321 Palindrome numbers: all 1,999, by length, with a finder Exact rule: L ≥ 2 and s reads the same backwards | 11 | 1,989 | 1 in 503 | 90 |
| Uphill Climb | Four or more digits in a row that keep going up, like 1359 Exact rule: s contains ≥ 4 consecutive digits, each strictly greater than the one before (e.g. 1359) | 1,234 | 50,022 | 1 in 20 | 43 |
| Downhill Slide | Four or more digits in a row that keep going down, like 8531 Exact rule: s contains ≥ 4 consecutive digits, each strictly smaller than the one before | 3,210 | 57,960 | 1 in 17 | 41 |
| Even Keel | Every digit is even (0, 2, 4, 6 or 8), like 4,826 Exact rule: every digit is 0, 2, 4, 6 or 8 | 0 | 15,625 | 1 in 64 | 60 |
| Odd Squad | Every digit is odd (1, 3, 5, 7 or 9), like 1,579 Exact rule: every digit is 1, 3, 5, 7 or 9 | 1 | 19,530 | 1 in 51 | 57 |
| Nine Sum | The digits add up to exactly 9, like 1,251 (1 + 2 + 5 + 1) Exact rule: the digits add up to exactly 9 | 9 | 2,002 | 1 in 500 | 90 |
| No Repeats | Two or more digits and no digit appears twice, like 795,014 Exact rule: L ≥ 2 and all digits are different | 10 | 168,561 | about 1 in 6 | 26 |
| Digits total | Badge awards in this family (a number can earn several) | 756,662 | |||
Primes 5 badges
| Badge | What it means | Example | Count | Odds | Points |
|---|---|---|---|---|---|
| Indivisible | A prime number: nothing but 1 and itself divides it evenly, like 97 Exact rule: n is prime | 2 | 78,498 | 1 in 13 | 37 |
| Twin Star | A prime with another prime just 2 away, like 41 (43 is prime too) Exact rule: n is prime and n − 2 or n + 2 is prime | 3 | 16,337 | 1 in 61 | 59 |
| Prime Parts | Every digit is 2, 3, 5 or 7 (the one-digit primes), like 7,253 Exact rule: every digit is 2, 3, 5 or 7 | 2 | 5,460 | 1 in 183 | 75 |
| Two Factors | Made by multiplying exactly two primes, like 15 (3 × 5) or 49 (7 × 7) Exact rule: n is the product of exactly two primes, counted with multiplicity (4, 6, 9, 10…) | 4 | 210,035 | about 1 in 5 | 23 |
| Square Pair | Two square numbers add up to it, like 25 (9 + 16) Exact rule: n ≥ 1 and n = a² + b² for integers a, b ≥ 0 | 1 | 216,340 | about 1 in 5 | 22 |
| Primes total | Badge awards in this family (a number can earn several) | 526,670 | |||
Shapes 9 badges
| Badge | What it means | Example | Count | Odds | Points |
|---|---|---|---|---|---|
| Square Deal | A whole number times itself, like 144 (12 × 12) Exact rule: n ≥ 1 is a perfect square | 1 | 999 | 1 in 1,001 | 100 |
| Cubed | A whole number times itself three times, like 125 (5 × 5 × 5) Exact rule: n ≥ 1 is a perfect cube | 1 | 99 | 1 in 10,101 | 133 |
| Triangle Stack | That many dots make a neat triangle (1, 3, 6, 10, 15…), like 55 Exact rule: n ≥ 1 is triangular, k(k+1)/2 | 1 | 1,413 | 1 in 708 | 95 |
| Golden Spiral | In the Fibonacci sequence, where each number adds the two before it (1, 2, 3, 5, 8, 13…), like 6,765 Exact rule: n ≥ 1 is a Fibonacci number | 1 | 29 | 1 in 34,483 | 151 |
| Factorial Flash | Multiply 1 × 2 × 3 × … up to some number and you get it, like 120 (1 × 2 × 3 × 4 × 5) Exact rule: n is k! for some k ≥ 1 (1, 2, 6, 24, 120, 720, 5040, 40320, 362880) | 1 | 9 | 1 in 111,111 | 168 |
| Doubling Up | Keep doubling from 1 and you reach it (1, 2, 4, 8, 16…), like 1,024 Exact rule: n is 2^k for k ≥ 0 | 1 | 20 | 1 in 50,000 | 156 |
| Flawless | Equals the sum of all its smaller divisors, like 28 (1 + 2 + 4 + 7 + 14) Exact rule: n is a perfect number (6, 28, 496, 8128) | 6 | 4 | 1 in 250,000 | 179 |
| Digit Divider | Divides evenly by the sum of its digits, like 81 (8 + 1 = 9, and 81 ÷ 9 = 9) Exact rule: n ≥ 1 is divisible by its digit sum (Harshad) | 1 | 95,427 | 1 in 10 | 34 |
| Kaprekar's Trick | Square it, cut the answer in two, and the halves add back up to it, like 45 (45 × 45 = 2025, and 20 + 25 = 45) Exact rule: n is a Kaprekar number (the original definition: n² split into a left part and a non-zero right part of L digits that sum to n; includes 1) | 1 | 50 | 1 in 20,000 | 143 |
| Shapes total | Badge awards in this family (a number can earn several) | 98,050 | |||
Constants 11 badges
| Badge | What it means | Example | Count | Odds | Points |
|---|---|---|---|---|---|
| Pi Crumb | Its 4 digits appear in a row in the first 1,000 digits of pi (3.14159…), like 1,415 Exact rule: L = 4 and s appears within the first 1,000 digits of π | 1,000 | 863 | 1 in 1,159 | 102 |
| Pi Bite | Its 5 digits appear in a row in the first 1,000 digits of pi (3.14159…), like 14,159 Exact rule: L = 5 and s appears within the first 1,000 digits of π | 10,003 | 897 | 1 in 1,115 | 101 |
| Pi Wedge | Its 6 digits appear in a row in the first 1,000 digits of pi (3.14159…), like 592,653 Exact rule: L = 6 and s appears within the first 1,000 digits of π | 100,031 | 903 | 1 in 1,107 | 101 |
| Euler Crumb | Its 4 digits appear in a row in the first 1,000 digits of Euler's number e (2.71828…), like 7,182 Exact rule: L = 4 and s appears within the first 1,000 digits of e | 1,011 | 852 | 1 in 1,174 | 102 |
| Euler Bite | Its 5 digits appear in a row in the first 1,000 digits of Euler's number e (2.71828…), like 71,828 Exact rule: L = 5 and s appears within the first 1,000 digits of e | 10,115 | 894 | 1 in 1,119 | 101 |
| Euler Wedge | Its 6 digits appear in a row in the first 1,000 digits of Euler's number e (2.71828…), like 718,281 Exact rule: L = 6 and s appears within the first 1,000 digits of e | 101,157 | 895 | 1 in 1,117 | 101 |
| Golden Crumb | Its 4 digits appear in a row in the first 1,000 digits of the golden ratio (1.61803…), like 6,180 Exact rule: L = 4 and s appears within the first 1,000 digits of φ | 1,011 | 856 | 1 in 1,168 | 102 |
| Golden Bite | Its 5 digits appear in a row in the first 1,000 digits of the golden ratio (1.61803…), like 61,803 Exact rule: L = 5 and s appears within the first 1,000 digits of φ | 10,117 | 895 | 1 in 1,117 | 101 |
| Golden Wedge | Its 6 digits appear in a row in the first 1,000 digits of the golden ratio (1.61803…), like 618,033 Exact rule: L = 6 and s appears within the first 1,000 digits of φ | 101,170 | 895 | 1 in 1,117 | 101 |
| Round Thousand | Ends in 000, like 42,000 Exact rule: n ≥ 1 is divisible by 1,000 | 1,000 | 999 | 1 in 1,001 | 100 |
| Round Ten Thousand | Ends in 0000, like 70,000 Exact rule: n ≥ 1 is divisible by 10,000 | 10,000 | 99 | 1 in 10,101 | 133 |
| Constants total | Badge awards in this family (a number can earn several) | 9,048 | |||
Calendar and clock 4 badges
| Badge | What it means | Example | Count | Odds | Points |
|---|---|---|---|---|---|
| US Date Stamp | Six digits that read as a US date, month then day then year, like 122590 (12/25/90) Exact rule: L = 6 and s is MMDDYY: MM 01–12, DD valid for that month; 29 Feb only if YY is divisible by 4 (00 counts, read as 2000) | 100,100 | 9,200 | 1 in 109 | 68 |
| World Date Stamp | Six digits that read as a date, day then month then year, like 251290 (25/12/90) Exact rule: L = 6 and s is DDMMYY, same validity rules | 100,100 | 25,725 | 1 in 39 | 53 |
| Year Marker | A year from 1900 to 2099, like 1969 Exact rule: L = 4 and 1900 ≤ n ≤ 2099 | 1,900 | 200 | 1 in 5,000 | 123 |
| Clock Face | Reads as a time on a 24-hour clock, like 1225 (12:25) or 945 (9:45) Exact rule: L = 4 and s is HHMM with HH 00–23, MM 00–59; or L = 3 and s is HMM with H 0–9, MM 00–59 | 100 | 1,380 | 1 in 725 | 95 |
| Calendar and clock total | Badge awards in this family (a number can earn several) | 36,505 | |||
Culture 12 badges
| Badge | What it means | Example | Count | Odds | Points |
|---|---|---|---|---|---|
| Seventh Heaven | The number 7 exactly Why: Seven is the number most often picked as "lucky" around the world. Exact rule: n equals 7 exactly | 7 | 1 | 1 in 1,000,000 | 199 |
| Baker's Dozen | The number 13 exactly Why: A baker's dozen is 13; many buildings still skip a 13th floor. Exact rule: n equals 13 exactly | 13 | 1 | 1 in 1,000,000 | 199 |
| Deep Thought | The number 42 exactly Why: The answer to life, the universe and everything in Douglas Adams's The Hitchhiker's Guide to the Galaxy. Exact rule: n equals 42 exactly | 42 | 1 | 1 in 1,000,000 | 199 |
| Hundred Club | The number 100 exactly Why: A perfect score, a century, the first three-digit number. Exact rule: n equals 100 exactly | 100 | 1 | 1 in 1,000,000 | 199 |
| Sevens Row | The number 777 exactly Why: Three sevens in a row, a long-standing symbol of luck. Exact rule: n equals 777 exactly | 777 | 1 | 1 in 1,000,000 | 199 |
| Thousand Nights | The number 1,001 exactly Why: One Thousand and One Nights, the story collection that gave us Aladdin and Sinbad. Exact rule: n equals 1001 exactly | 1,001 | 1 | 1 in 1,000,000 | 199 |
| Elite Code | The number 1,337 exactly Why: Early internet slang spelling "elite" with digits. Exact rule: n equals 1337 exactly | 1,337 | 1 | 1 in 1,000,000 | 199 |
| Tile Merger | The number 2,048 exactly Why: 2¹¹, and the target tile in the 2014 sliding-number puzzle. Exact rule: n equals 2048 exactly | 2,048 | 1 | 1 in 1,000,000 | 199 |
| Power Level | The number 9,001 exactly Why: "Over nine thousand!", one of the internet's oldest anime memes. Exact rule: n equals 9001 exactly | 9,001 | 1 | 1 in 1,000,000 | 199 |
| Pi Opening | The number 314,159 exactly Why: The first six digits of π. Exact rule: n equals 314159 exactly | 314,159 | 1 | 1 in 1,000,000 | 199 |
| Count Off | The number 123,456 exactly Why: The full counting run, and still the world's most common password. Exact rule: n equals 123456 exactly | 123,456 | 1 | 1 in 1,000,000 | 199 |
| Top Shelf | The number 999,999 exactly Why: The highest number you can roll. Exact rule: n equals 999999 exactly | 999,999 | 1 | 1 in 1,000,000 | 199 |
| Culture total | Badge awards in this family (a number can earn several) | 12 | |||
All families: 53 badges, 1,426,947 badge awards across 1,000,000 numbers. 179,035 numbers earn no badge.
Check any number in the Rarebit number calculator, or roll today’s number.