The puzzle as presented earlier this week:
The other evening at dinner, Max and Nora were counting out numbers on their fingers. Max, age five (almost six!) was using both hands to count to ten — making base 10 numbers. Nora, on the other hand, just turned three, and was counting in a less traditional method. She counted from one to ten, and then made “two hand” two-digit numbers, counting ten (1-0) to fifteen (1-5), and then jumped to twenty (2-0) through twenty five (2-5.) She was stumped at fifty-five (5-5), and then borrowed one of my fingers to start again at one-hundred (1-0-0.)
With the eight hands at the table, as my dear wife was with us of course, we could count in this manner up to 55,555,555, the largest 8-digit number represented upon fingers. This week’s GeekDad Puzzle of the Week is once again straightforward — if we did indeed count from zero (00,000,000) to this MaxInt (pun intended) of 55,555,555 with no single digit larger than a hand’s count of digits (five), how many primes would we encounter? Note that for purposes of this puzzle, any given number’s divisors need not be representable on fingers. That is, 35 (a number we would encounter) is still composite despite us not being able to represent one of its divisors, 7. Standard base 10 multiplication and division rules still apply.
There were many methods described to solve this week’s puzzle, from custom Python code snippets sent to leveraging a modified Sieve of Erastosthenes. This week’s most elegant solution was also the one selected at random from the winning set. Congratulations to Cole Lodge, who applied on old school “grep” command to a list of primes pulled directly from the University of Tennessee at Martin’s “The Prime Pages,” my personal source of prime numbers and prime related trivia for years now. Cole correctly ascertained that we would encounter some 83,664 prime numbers counting from 0 to 55,555,555 using only digits representable on our digits. His answer (and luck) earned him this week’s $50 ThinkGeek gift certificate.
Many thanks to everyone that posted a solution, and good luck with this week’s puzzle!
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