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IMAS 2023/2024 - Middle Primary - First Round Question 9

IMAS · IMAS 2023/2024 - Middle Primary - First Round

Question 9

Four poker cards are randomly drawn from a deck. The goal is to combine the values of these cards by using the four arithmetic operators ($+$, $-$, $\times$ and $\div$) to obtain 24. It is assumed that A, J, Q and K have the values of 1, 11, 12 and 13, respectively. For example, if the four cards are shown below, one way to get 24 is $12\div(13-11)\times4=24$.

Question illustration

Now, there are five piles of cards, where four cards are in each pile:

Question illustration

For how many of these piles can get 24 by using the conditions stated above?
  1. 5
  2. 4
  3. 3
  4. 2
  5. 1