Chocolates

Number Theory Level pending

Box P has p p chocolates and box Q Q has q q chocolates, where p p and q q are both odd and p > q p> q .

What is the smallest number of chocolates which would have to be moved from box P to box Q so that box Q has more chocolates than box P?

Source: UKMT.
p + q + 2 2 \frac{p+q+2}2 q − p + 2 2 \frac{q-p+2}2 q + p − 2 2 \frac{q+p-2}2 p − q − 2 2 \frac{p-q-2}2 p − q + 2 2 \frac{p-q+2}2

Hill Taeudomkul by Hill Taeudomkul , 19, Thailand

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