MathDB
Median-ception

Source: 2017 AIME I #11

March 8, 2017
AMCAIMEAIME I2017 AIME Icombinatoricsgrids

Problem Statement

Consider arrangements of the 99 numbers 1,2,3,…,91, 2, 3, \dots, 9 in a 3×33 \times 3 array. For each such arrangement, let a1a_1, a2a_2, and a3a_3 be the medians of the numbers in rows 11, 22, and 33 respectively, and let mm be the median of {a1,a2,a3}\{a_1, a_2, a_3\}. Let QQ be the number of arrangements for which m=5m = 5. Find the remainder when QQ is divided by 10001000.
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