Self-Referencing English Number

Computer Science Level pending

Suppose we want to convert a positive integer into a word in American English spelling, and hyphens are treated as spaces, and compute its word product , which is simply the product of lengths of each word formed.

For example,

  • The number 24 can be written as twenty four , its word product is W P ( 24 ) = 6 × 4 = 24. W_P(24) = 6\times 4 = 24.

  • The number 1011 can be written as one thousand eleven , so W P ( 1011 ) = 3 × 8 × 6 = 144 W_P(1011) = 3\times 8\times6 = 144 .

Find a 14-digit positive integer N N such that W P ( N ) = N . W_P(N) = N .

See Part 2 and Part 3 here.


The answer is 92215733299200.

Jonathan Pappas by Jonathan Pappas , 19, USA

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1 solution

Jonathan Pappas
Nov 18, 2020

92215733299200 92215733299200 is the answer.

92215733299200 92215733299200 expanded into English is:

  • Ninety two trillion two hundred fifteen billion seven hundred thirty three million two hundred ninety nine thousand two hundred

When you multiply the length of each word together 6 ∗ 3 ∗ 8 ∗ 3 ∗ 7 ∗ 7 ∗ 7 ∗ 5 ∗ 7 ∗ 6 ∗ 5 ∗ 7 ∗ 3 ∗ 7 ∗ 6 ∗ 4 ∗ 8 ∗ 3 ∗ 7 = 92215733299200 6 * 3 * 8 * 3 * 7 * 7 * 7 * 5 * 7 * 6 * 5 * 7 * 3 * 7 * 6* 4 * 8 * 3 * 7 = 92215733299200

Amazing. (How many other numbers share this quality?)

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