TxO Math Bowl 2024 - Team Contest - Problem 13


Let a,b,c,da, b, c, d be non-negative reals such that a+b+c+d=12a + b + c + d = 12. If the sum of the maximum and the minimum value of a+1+2b+1+3c+1+6d+1{a + 1} + \sqrt{2b + 1} + \sqrt{3c + 1} + \sqrt{6d + 1}

can be expressed as p+q+rsp + \sqrt{q} + r\sqrt{s}, where pp, qq, rr, and ss are positive integers, and qq and ss are not divisible by the square of any prime, compute p+q+r+sp + q + r + s.

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Category: TxO Math Bowl Team Contest
Points: 4
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