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UKMT Senior Kangaroo, 2023

Combinatorics Difficulty 2.0 Junior Prove it United Kingdom

Five cards have the numbers $101$ , $102$ , $103$ , $104$ and $105$ on their fronts. On the reverse, each card has a statement printed as follows: 101: The statement on card 102 is false. 102: Exactly two of these cards have true statements. 103: Four of these cards have false statements. 104: The statement on card 101 is false. 105: The statements on cards 102 and 104 are both false. What is the total of the numbers shown on the front of the cards with TRUE statements?

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