Problem 25 · 2020 Math Kangaroo
Stretch
Counting & Probability
Logic & Word Problems
careful-countingcasework
Ten people each order an ice cream: four vanilla, three chocolate, two lemon and one mango. As toppings they order four umbrellas, three cherries, two wafers and one chocolate gum — one topping per ice cream. Since no two of the ten ice creams may be exactly alike, which of the following combinations is possible?
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Answer: E — Lemon and cherry.
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Hint 1 of 2
Each flavour gets a different topping, with limited supply (4 umbrellas, 3 cherries, 2 wafers, 1 gum).
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Hint 2 of 2
A pairing is impossible if it forces two identical ice creams or runs a topping short.
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Approach: test each pairing against the flavour and topping counts
- Ten ice creams (4 vanilla, 3 chocolate, 2 lemon, 1 mango) each get a distinct topping (4 umbrellas, 3 cherries, 2 wafers, 1 gum), no two identical.
- Each option claims a specific flavour-topping pair; check it can fit a full valid assignment.
- Only option E (lemon with cherry) is consistent with completing the whole table.
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