Problem 15 · 2015 Math Kangaroo
Medium
Counting & Probability
careful-counting
Two of the 5 ladybirds in the picture are always friends with each other if the difference between their number of dots is exactly 1. Today every ladybird has sent an SMS to each of their friends. How many SMS messages were sent?
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Answer: C — 6
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Hint 1 of 2
First count the spots on each ladybird, then pair up those that differ by exactly one spot.
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Hint 2 of 2
Each friendship means two messages, since each friend texts the other.
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Approach: find friend pairs, then count messages both ways
- The ladybirds carry 2, 3, 3, 5 and 6 spots.
- Friends differ by exactly 1 spot: the 2-spot is friends with each 3-spot, and the 5-spot is friends with the 6-spot — 3 friendships in all.
- In each friendship both friends send a message, so each pair accounts for 2 messages.
- Total messages: 3 × 2 = 6.
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