Problem 21 · 2023 Math Kangaroo
Medium
Spatial & Visual Reasoning
spiral-patternsequence-of-figures
The diagram shows a spiral of consecutive numbers starting with 1. In which order will the numbers 625, 626 and 627 appear in the spiral? (Choose the matching arrangement A–E shown below.)
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Answer: B
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Hint 1 of 3
Perfect squares sit at the corners of a square spiral, so note that \(625 = 25^2\).
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Hint 2 of 3
Decide which side of the spiral the run 625–627 lies on, and exactly where the spiral turns its next corner.
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Hint 3 of 3
Find whether 625 to 626 is a straight step and where the right-angle turn to 627 happens.
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Approach: use that 625 is a perfect square sitting just before a corner
- Since \(625 = 25^2\), it lands on a straight arm of the spiral with a corner just ahead.
- Following the winding, 625 and 626 line up along that arm (626 directly past 625), and the spiral then turns a right angle so 627 steps off perpendicular to the 625–626 segment.
- That straight pair plus a perpendicular third number is exactly the arrangement in option B.
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