Problem 21 · 2010 Math Kangaroo
Stretch
Logic & Word Problems
work-backwardcareful-counting
To decide who gets the last piece of Leni’s birthday cake, five children use a counting rhyme. Leni, Sara, Hannes, Petra and Arno stand in this order, clockwise in a circle. They count clockwise: KAN – GA – ROO – OUT – ARE – YOU. One child is counted for each syllable, and whoever is counted on YOU is out. They repeat this until only one child is left. Leni may choose who starts the count. Whom must she choose if she wants Arno to get the piece of cake?
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Answer: B — Sara
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Hint 1 of 2
The rhyme has 6 syllables, so count 6 children around the circle and the 6th one is out.
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Hint 2 of 2
Try each possible starting child and act it out around the circle until one child is left — you want that to be Arno.
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Approach: act it out starting with Sara
- Start the count on Sara: counting 6 (Sara, Hannes, Petra, Arno, Leni, Sara) puts Sara out.
- Keep going from the next child each time: the next two rounds put Petra out, then Hannes out.
- That leaves Leni and Arno, and the final count of 6 puts Leni out, so Arno survives — Leni must choose Sara (answer B).
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