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        riddles >> putnam exam (pure math) >> Palindrome
        
(Message started by: dsd on Mar 6^th, 2010, 12:52am)

Title: Palindrome
Post by dsd on Mar 6^th, 2010, 12:52am

Hello everyone!!! could you guy takes a look at this problem for me??? I'm totally lost... thnx...

A palindrome is a number that reads the same forwards as backwards. Give the next three palindrome number after a₁a₈a₆a₃a₂a₄a₈a₈that are divisible by 3, and explain your method for finding them.

(For example, the next palindrome number after 119 is 121, and the next after that is 131, etc.
Do not count leading O's as part of a number.)

next three:___________________________

How did you find them?? Explain please....... ;D

Title: Re: Palindrome
Post by Grimbal on Mar 8^th, 2010, 2:03am

on 03/06/10 at 00:52:18, dsd wrote:

a₁a₈a₆a₃a₂a₄a₈a₈

what do you mean by this?

Quote:

(For example, the next palindrome number after 119 is 121, and the next after that is 131, etc.

But 121 and 131 are not divisible by 3.

The trick would be to take the first half of the digits and create a sequence from that. The rest is just a mirror image.
For example, starting from
339374545
you take the first half (rounded up)
33937
and start counting
33937 -> 339373933
33938 -> 339383933
33939 -> 339393933
33940 -> 339404933
33941 -> 339414933
then make sure the first is > the initial number and keep only the multiple of 3.