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sum game 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13

Source: XV May Olympiad (Olimpiada de Mayo) 2009 L2 P3

September 19, 2022
algebra

Problem Statement

In the following sum: 1+2+3+4+5+61 + 2 + 3 + 4 + 5 + 6, if we remove the first two “+” signs, we obtain the new sum 123+4+5+6=138123 + 4 + 5 + 6 = 138. By removing three “++” signs, we can obtain 1+23+456=4801 + 23 + 456 = 480. Let us now consider the sum 1+2+3+4+5+6+7+8+9+10+11+12+131 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13, in which some “++” signs are to be removed. What are the three smallest multiples of 100100 that we can get in this way?
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