GeekDad Puzzle of the Week – Regular Palindrome Numbers

Regular numbers are numbers that evenly divide powers of 60. As an example, 60² = 3600 = 48 × 75, so both 48 and 75 are divisors of a power of 60. They are reasonably rare — under 10⁸, there are just over 1100 of them.

Symmetric or “palindrome” numbers are numbers that read forward and backwards as the same number: in bases 10 and 2, the decimal number 33 (aka 100001₂) reads the same in both directions.

This week’s GeekDad Puzzle of the Week is straightforward: How many decimal numbers under 10⁸ are regular, and are also palindromes in at least one base from 2 to 10?

NOTE: Leading zeros don’t count towards symmetry, so 012303210₃ is not symmetric in base 3.

As always, send your response into GeekDad Central, and the winner will be chose from among the correct (or at least reasonably reasoned) answers sent in. This week’s prize is yet another fabulous $50 Gift Certificate from our fine friends over at ThinkGeek.

Good luck, and happy puzzling!