Saturday, January 24, 2015

Bad Johnny

As punishment for misbehaving, Johnny's teacher made him write out the number words from ONE to ONE MILLION. When Johnny was finished, the teacher asked him how many times he had written the letter A. "That one's easy," Johnny said. "A more interesting question is why I wrote the same number of Gs as Xs."

"Smarty pants," said the teacher. "You forgot to mention W."

1 comment:

jeff said...

Count(A) = 999,000.
A appears exactly once in the word THOUSAND, which is used exactly once in every number >999, except for ONE MILLION.
999,999 – 999 = 999,000

I haven't figured out W's uniqueness or how to state a proof that Count(X) = Count(G) other than the former is only used exactly once for each 6 and the same is true for G and 8. It seems self-evident that there are exactly as many uses of each digit within the stated range.

I believe W follows the same pattern as X and G because it appears only once per word used for each 2 (TWO, TWELVE, TWENTY).

By the way, M is used only once: ONE MILLION.

The zero-use letters cluster / spread in a way that reminds me of prime #s:
B,C, J,K, P,Q, Z