MathDB

In the mathematical talent show called “The

X^2

-factor” contestants are scored by a a panel of

8

judges. Each judge awards a score of

0

(‘fail’),

X

(‘pass’), or

X^2

(‘pass with distinction’). Three of the contestants were Ann, Barbara and David. Ann was awarded the same score as Barbara by exactly

4

of the judges. David declares that he obtained different scores to Ann from at least

4

of the judges, and also that he obtained different scores to Barbara from at least

4

judges.
In how many ways could scores have been allocated to David, assuming he is telling the truth?

Problem Statement