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forum.virtualchallengemeets.com • View topic - AIME I #6 2008

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AIME I #6 2008

American Mathematics Contest & American Invitational Mathematics Examination. See for more information
Note:USAMO/IMO-level questions need to go in the Olympiad section.
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AIME I #6 2008

Postby stupidityismygam » Tue Mar 25, 2008 5:49 pm

A triangular array of numbers has a first row consisting of the odd integers [unparseable or potentially dangerous latex formula] in increasing order. Each row below the first has one fewer entry than the row above it, and the bottom row has a single entry. Each entry in any row after the top row equals the sum of the two entries diagonally above it in the row immediately above it. How many entries in the array are multiples of [unparseable or potentially dangerous latex formula]?
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Re: AIME I #6 2008

Postby Dragon of Light » Sun Mar 30, 2008 6:53 pm

Clearly, the only odd number between 1 and 99 that is a multiple of 67 is 67.

Thus, the answer is 17.
Record UIL/TMSCA scores:

Number Sense: 4 (2007 District UIL)
Calculator: 29 (2008 District UIL)
General Math: -30 (2008 TMSCA State)
Science: -81 (2007 TMSCA State)
CompSci: 7 (2008 District UIL)

I'm rather proud of my Calculator score. I broke 10.
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