Problem 21 · 2019 Math Kangaroo
Stretch
Counting & Probability
total-then-divide
Emil takes selfies with his 8 cousins. Each one of the 8 cousins appears in two or three of the pictures. There are exactly 5 cousins in each picture. How many selfies does Emil take?
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Answer: B — 4
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Hint 1 of 3
Count the total number of 'cousin appearances' — every face that shows up in every photo.
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Hint 2 of 3
Since each cousin appears 2 or 3 times, this total must be between 2×8 and 3×8.
Still stuck? Show hint 3 →
Hint 3 of 3
Each photo shows exactly 5 cousins, so the number of photos times 5 equals that total.
Show solution
Approach: count total appearances, then divide by 5
- Each of the 8 cousins shows up 2 or 3 times, so the total number of cousin-appearances is between 2×8 = 16 and 3×8 = 24.
- Each photo holds exactly 5 cousins, so the number of photos times 5 must land between 16 and 24 — only 5 × 4 = 20 works.
- So there are 4 photos (20 appearances split as four cousins thrice and four cousins twice): Emil takes 4 selfies (B).
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