Problem 22 · 2023 Math Kangaroo
Stretch
Counting & Probability
careful-countingcasework
Martin has three cards, each labelled with a number on both sides (see picture: front and back). He places the three cards on the table without paying attention to which side is up, and adds the three numbers he can see. How many different sums can Martin get this way?
Show answer
Answer: E — A different amount.
Show hints
Hint 1 of 2
Each card shows one of its two numbers, so there are a few possible visible triples to add up.
Still stuck? Show hint 2 →
Hint 2 of 2
List every possible sum, then count how many different totals there really are and compare with the choices.
Show solution
Approach: list all visible triples and count the distinct sums
- Each card shows either its front or back number: card 1 shows 1 or 4, card 2 shows 2 or 5, card 3 shows 3 or 6.
- Notice each card's two numbers differ by 3, so the sum changes by 3 each time a card is flipped; the possible sums are 6, 9, 12 and 15.
- That is 4 different sums.
- Since 4 is not among the listed choices, the answer is E, a different amount.
Mark:
· log in to save