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Problem 429

Combinatorics Difficulty 2.0 Find the answer UKMT Grey Kangaroo · United Kingdom · 2024

Nine cards numbered from 1 to 9 were placed facedown on the table. Aleksa, Bart, Clara and Deindra each picked up two of the cards. Aleksa said, “My numbers add up to 6.” Bart said, “The difference between my numbers is 5.” Clara said, “The product of my numbers is 18.” Deindra said, “One of my numbers is twice the other one.” All four made a true statement. Which number was left on the table?

(A) $1$ (B) $3$ (C) $6$ (D) $8$ (E) $9$

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