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2015 CIMC keystage2-EMIC individual Question 2

xIMC · 2015 CIMC keystage2-EMIC individual

Question 2

Each students is asked to remove three of the first twenty-one positive integers $(1,2,3,\ldots,21)$ and calculate the sum of the remaining eighteen numbers. The three numbers removed by each student contain two consecutive numbers, and no two students remove the same three numbers. At most how many students can correctly get $212$ as the answer?