Question

Mr. Zhou places all the integers from $1$ to $225$ into a $15$ by $15$ grid. He places $1$ in the middle square (eighth row and eighth column) and places other numbers one by one clockwise, as shown in part in the diagram below. What is the sum of the greatest number and the least number that appear in the second row from the top?

$367$

$368$

$369$

$379$

$380$

Answer: A

Concepts:pattern recognition perfect square

Difficulty rating: 1420

Video solution:

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Written solution:

In the outer $15\times15$ ring, the top row contains $211,212,\ldots,225,$ so the number just below $211$ in the second row is $210.$ This is the greatest number in the second row.

The inner $13\times13$ spiral has $13^2=169$ in its upper-right corner. In the second row of the full grid, the inner-ring entries run from $157$ to $169.$ Thus the least entry in that row is $157.$

The required sum is $210+157=367.$

Thus, the answer is A .

2021 AMC 10B Spring Problem 8

Answer: A

Difficulty rating: 1420

Video solution:

Written solution:

Problem 8 in Other Years