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tmua.me Extreme Set A Paper 2 · Q9

Paper 2GeometrySequences & series

Five boxes are arranged in a circle. In clockwise order, their initial numbers of counters are

0,1,0,2,4.0,\quad1,\quad0,\quad2,\quad4.

In one move, two adjacent boxes are chosen and one counter is added to each of them. The first and fifth boxes in the displayed order are adjacent. Counters are never removed.

What is the complete set of integers nn for which a finite sequence of moves can leave exactly nn counters in each box?

AAll integers n≥4n\ge4
BAll odd integers n≥5n\ge5
CAll odd integers n≥7n\ge7
DAll integers n≥7n\ge7
EAll even integers n≥8n\ge8
FAll odd integers n≥9n\ge9

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