Problem 3 · 2020 Math Kangaroo
Medium
Spatial & Visual Reasoning
spatial-reasoning
When Cosme correctly wears his new shirt, as shown in the left figure, the horizontal stripes form seven closed arches around his body. This morning he buttoned his shirt in the wrong way, as shown on the right. How many open arches were there around Cosme’s body this morning?
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Answer: B — 1
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Hint 1 of 2
A closed arch needs its stripe to line up on both sides of the button placket; an open arch is one that no longer meets.
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Hint 2 of 2
Misbuttoning slides one half of the shirt up by a single button, so trace which of the seven arches still join.
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Approach: track how the one-button shift breaks the stripe matches
- Buttoning wrong slides the two halves of the shirt past each other by one button.
- Each stripe then meets the stripe one position over, so almost every arch still closes — just one level higher.
- Following the figure, only the single arch at the very bottom is left with nothing to meet, so it stays open.
- So the number of open arches is 1, choice B.
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