Problem 13 · 2023 Math Kangaroo
Stretch
Logic & Word Problems
work-backwardcareful-counting
Each of the children Ali, Lea, Josef, Vittorio and Sophie gets a birthday cake. The number on top of the cake shows how old the child is. Lea is two years older than Josef, but one year younger than Ali. Vittorio is the youngest. Which cake belongs to Sophie?
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Answer: C
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Hint 1 of 3
There are five cakes with five ages on them — match a child to each one.
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Hint 2 of 3
Use the clues to label the easy children first, and give the smallest cake to Vittorio.
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Hint 3 of 3
Sophie gets the one cake that is left over after everyone else is matched.
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Approach: match the easy children first; Sophie gets the leftover cake
- Josef, then Lea (2 older than Josef), then Ali (1 older than Lea) line up in a row of ages.
- Vittorio is the youngest, so he takes the smallest-numbered cake.
- Four children are now placed, so the one cake left over is Sophie's: the cake showing 6, option C.
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