FOR GROWNUPS

PROBLEM # 2
A palindromic number is a whole number that is the same number forwards as it is backwards. For example, 151 is a palondromic number. There are 90 three digit palindromes. How many five-digit palindromes exist?

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SOLUTIONS TO PROBLEMS ON 10/21/04

FOR CHILDREN

PROBLEM # 1

How many cubic inches of dirt were there in a hole that is one foot deep, two feet wide, and three feet long?

SOLUTION
10,368 cubic inches.

FOR GROWNUPS

PROBLEM # 2

Find the maximum integer value of N for which N! ends in 2004 zeros.

SOLUTION
This problem turned out to be lot harder than expected. This problem appeared recently in the MA High School Math League. I had multiple answers submitted. The answer is: 8029.

Every 5 numbers yield one factor of 5, every 25 yield an extra for 6, every 125 yield 31, every 625 yield 156 and every 3125 yield 781 fives. To get 2005 zeros we need 2(3125) + 2(625) + 4(25) +1(25) + 1(5) or 8030 so 8030! ends in 2005  zeros and the answer is 8029.

Congratulations to Madhu Gandhi, Nidhee Krishnan, Anupa M., Amisha Nehra, Rajiv Ramaratnam, Mukund Seshadri, Sumanth Shankar, Wajida Syed and Rajesh Viswanathan, who were winners of the last set of puzzles.