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UKMT Junior Kangaroo, 2022

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

A rubber ball falls from the roof of a house of height 10 m. Each time it hits the ground, it rebounds to four-fifths of the height it fell from previously. How many times will the ball appear in front of a 1 m high window whose bottom edge is 5 m above the ground?

(A) $1$ (B) $2$ (C) $4$ (D) $6$ (E) $8$

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