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Find the number of ordered pairs of positive integers (x1, x2, x3, y1, y2) satisfying the equation (x1 + x2 + x3)(y1 + y2) = 77.
- 150
- 270
- 420
- 1024
Correct answer: 420
Solution
We write 77 as a product of two positive integers (p)(q) and count compositions: C(p-1,2) ways for x1+x2+x3=p and C(q-1,1) ways for y1+y2=q, then sum over all factorizations.
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