Problem 17 · 2025 Math Kangaroo
Hard
Logic & Word Problems
sum-constraintwork-backward
Six ladybirds have 1, 2, 3, 4, 5 and 6 spots. Marta takes four photos, each showing three different ladybirds, and each ladybird appears in the same number of photos. The first three photos are shown. How many spots do the three ladybirds in the fourth photo have in total?
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Answer: C — 12
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Hint 1 of 2
There are 4 photos with 3 ladybirds each, that is 12 ladybird-appearances shared equally among 6 ladybirds.
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Hint 2 of 2
So every ladybird appears in exactly 2 photos, which tells you the grand total of spots over all four photos.
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Approach: find the grand total of all four photos, then subtract the three shown
- Four photos with three ladybirds each give 12 appearances; split equally among 6 ladybirds, so each appears in exactly 2 photos.
- Then all four photos together show every spot-count twice: 2 × (1 + 2 + 3 + 4 + 5 + 6) = 2 × 21 = 42 spots.
- The three shown photos hold 30 spots in total.
- So the fourth photo has 42 − 30 = 12 spots, option C.
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