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UKMT Pink Kangaroo, 2023

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

On the table there is a tower made of blocks numbered from $1$ to $90$ , as shown on the left of the diagram. Yett takes blocks from the top of the tower, three at a time, to build a new tower, as shown on the right of the diagram. How many blocks will be between blocks $39$ and $40$ when he has finished building the new tower?

(A) $0$ (B) $1$ (C) $2$ (D) $3$ (E) $4$

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