Home Competitions BALTIC-WAY 2009 Problem 2
BALTIC-WAY 2009 Problem 2
Let a 1 , a 2 , … , a 100 a_1,a_{2},\ldots ,a_{100} a 1 , a 2 , … , a 100 a 1 ⋅ ( a 1 − 1 ) ⋅ … ⋅ ( a 1 − 20 ) + a 2 ⋅ ( a 2 − 1 ) ⋅ … ⋅ ( a 2 − 20 ) + … + a 100 ⋅ ( a 100 − 1 ) ⋅ … ⋅ ( a 100 − 20 ) ≤ 100 ⋅ 99 ⋅ 98 ⋅ … ⋅ 79. a_1\cdot (a_1-1)\cdot\ldots\cdot (a_1-20)+a_2\cdot (a_2-1)\cdot\ldots\cdot (a_2-20)+ \ldots+a_{100}\cdot (a_{100}-1)\cdot\ldots\cdot (a_{100}-20)\le 100\cdot 99\cdot 98\cdot\ldots\cdot 79. a 1 ⋅ ( a 1 − 1 ) ⋅ … ⋅ ( a 1 − 20 ) + a 2 ⋅ ( a 2 − 1 ) ⋅ … ⋅ ( a 2 − 20 ) + … + a 100 ⋅ ( a 100 − 1 ) ⋅ … ⋅ ( a 100 − 20 ) ≤ 100 ⋅ 99 ⋅ 98 ⋅ … ⋅ 79. a 1 + a 2 + … + a 100 ≤ 9900 a_1+a_2+\ldots+a_{100}\le 9900 a 1 + a 2 + … + a 100 ≤ 9900
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