James Grime: 23 and Football Birthdays: Birthday Problem (誕生日のパラドックス)

Command:

$ bc <<< 'scale=10;364/365 * 363/365 * 362/365 * 361/365 * 360/365 * 359/365 * 358/365 * 357/365 * 356/365 * 355/365 * 354/365 * 353/365 * 352/365 * 351/365 * 350/365 * 349/365 * 348/365 * 347/365 * 346/365 * 345/365 * 344/365 * 343/365'

Result:

.4927027648

Ria Symonds: 7 and Happy Numbers (ハッピー数)

Example: 7

7
7^2 = 49
4^2 + 9^2 = 16 + 81 = 97
9^2 + 7^2 = 81 + 49 = 130
1^2 + 3^2 + 0^2 = 1 + 9 + 0 = 10
1^2 + 0^2 = 1 + 0 = 1

7 is a happy number


Example: 8

8
8^2 = 64
6^2 + 4^2 = 36 + 16 = 52
5^2 + 2^2 = 25 + 4 = 29
2^2 + 9^2 = 4 + 81 = 85
8^2 + 5^2 = 64 + 25 = 89
8^2 + 9^2 = 64 + 81 = 145
1^2 + 4^2 + 5^2 = 1 + 16 + 25 = 42
4^2 + 2^2 = 16 + 4 = 20
2^2 + 0^2 = 4 + 0 = 4
4^2 = 16
1^2 + 6^2 = 1 + 36 = 37
3^2 + 7^2 = 9 + 49 = 58
5^2 + 8^2 = 25 + 64 = 89

8 is not a happy number

Introducing the D-Wave 2X

James Grime: 14 Super Bowl Coin Tosses

Number of games you have to wait before you have 3 wins in a row:

t = 1/2(1+t) + 1/4(2+t) + 1/8(3+t) + 1/8(3)
t = 14

Number of games you have to wait before you have 14 wins in a row:

t = 1/2(1+t) + 1/4(2+t) + 1/8(3+t) + 1/16(4+t) + ... + 1/16384(14+t) + 1/16384(14)
t = 2 ^ (n+1) - 2
t = 32766

Three Dog Night: One (is the Loneliest Number)

James Grime: 1 and Prime Numbers: Fundamental theorem of arithmetic (算術の基本定理)

Thomas Woolley: 3/4 and Kleiber's Law

Thomas Woolley

• Max Kleiber

Roger Bowley and James Grime: Root 2: Square root of 2 (2の平方根)

James Grime: 17 and Sudoku Clues

• Gary McGuire

Matt Parker: 98 and Grafting Numbers

• Grafting number
• 3 - √5

3 - √5

James Clewett: 15 and Hexadecimal

Matt Parker: 3435: Munchausen number

Matt Parker

James Grime: 31 and Mersenne Primes (メルセンヌ数)

Yuki Usami (宇佐美佑果): 熱唱「ビバスポ！」テーマ曲

Yuki Usami