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MIT PRIMES/Art of Problem Solving

CROWDMATH 2017: The Broken Stick Problem

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mmaotmh   0
Sep 17, 2018
It appears to me that the thread you are looking at is using n as the number of breaks, but the question defines n as the number of pieces.
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mmaotmh
Sep 17, 2018
0 replies
A generalization of Problem 7
GeronimoStilton   0
Dec 29, 2017
$a+b$ players play the following game consisting of $n - 1$ turns. Alice's $a$ clones and Bob's $b$ clones go in some order. After all turns have passed, there are $n$ pieces. What is the maximum number of triangles that Alice's clones can guarantee forming given that Bob's clones are working against Alice's clones?

Clarification: One possible ordering might be $a_1,b_1,a_2,b_2,b_3$, which would repeat, and so for the first $6$ turns in this example, Alice's clones and Bob's clones would follow the sequence $a_1,b_1,a_2,b_2,b_3,a_1$.
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GeronimoStilton
Dec 29, 2017
0 replies
Finding the Minimum
RadioActive   6
N Dec 27, 2017 by RadioActive
Instead of asking for the maximum number of triangles Alice can make, I think it might also be interesting if we ask for the minimum. What do you guys think?
6 replies
RadioActive
Dec 14, 2017
RadioActive
Dec 27, 2017
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