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UKMT Intermediate Mathematical Challenge, 2020

Algebra Difficulty 2.0 Junior Find the answer United Kingdom

The Knave of Hearts stole some tarts. He ate half of them, and half a tart more. The Knave of Diamonds ate half of what was left, and half a tart more. Then the Knave of Clubs ate half of what remained, and half a tart more. This left just one tart for the Knave of Spades. How many tarts did the Knave of Hearts steal?

(A) $63$ (B) $31$ (C) $19$ (D) $17$ (E) $15$

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