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finallyskeptic · Post by **finallyskeptic** » Wed Nov 28, 2012 8:03 pm

Ohk so I logged in after two years.That doesn't matter. Here is a brainteaser that I came across a while back.Robert is giving his exams which comprises of 4 subjects lets say ABCD. The max he can score in A B and C are 50 each and he can score 100 in D.In how many ways can he score 150 ?

Gord · Post by **Gord** » Thu Nov 29, 2012 3:51 am

Hi.

I don't know. That sounds like math.

I assume the scores are given out in integers ranging from 0 to 50 (or 0 to 100) and no fractions? And not simply pass/fail, either 0 or 50 (or 0 or 100) with nothing in between?

finallyskeptic · Post by **finallyskeptic** » Thu Nov 29, 2012 7:30 am

Yeah only integers are allowed.No fractions please.All the integers including 0 and maximum are allowed.
A [0,50]
B [0,50]
C [0,50]
D [0,100]

IBelieve · Post by **IBelieve** » Wed May 01, 2013 11:38 am

1 way with a score of 0 for D.
3 ways with a score of 1 for D. [+2 more than previous.]
6 ways ... 2 for D. [+3 more than previous.]
...
+ ? ways ... 100 for D. [+101 more than previous.]
-------------------------------------------------------------------
= the answer.

= a0 + a1 + a2 + a3 + ...... + a100
= 1 + 1 + 2 + 1 + 2 + 3 + 1 + 2 + 3 + 4 + ....
= 1x101 + 2x100 + 3x99 + ... + 51x51 + 52x50 + ... + 101x1
= 2 x [1x101 + 2x100 + ... + 50x52] + 51x51
= 2 x sum from 0 to 49 of [1+i ][101-i] + 51x51
= 2 x sum from 0 to 49 of [101 + 100xi - ixi] + 51x51
= 2 x (50x101 + 100x49x50/2 - 49x50x99/6) + 51x51
= 176,851

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