For The Mathematically Inclined

A car travels downhill at 72 mph (miles per hour), on the level at 63 mph, and uphill at only 56 mph The car takes 4 hours to travel from town A to town B. The return trip takes 4 hours and 40 minutes.

PROBLEM #2
The sum of three numbers is 6, the sum of their squares is 8, and the sum of their cubes is 5. What is the sum of their fifth powers?

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Problems from 12/22/11

PROBLEM # 1
A perfect square has length n if its last n (decimal) digits are the same and non-zero. What is the maximum possible length? Find all squares that achieve this length.

SOLUTION 1

PROBLEM #2
What is the smallest positive integer such that when its last digit is moved to the start of the number (example: 1234 becomes 4123) the resulting number is larger than and is an integral multiple of the original number. Numbers are written in standard decimal notation, with no leading zeroes.

SOLUTION 2

Congratulations to Amit Joshi, who was the winner of the last set of puzzles.