MathCool #2

Logic Level 3

9 1 7 2 1 3 8 4 7 5 5 6 2 7 7 8 6 9 3 \LARGE{9|_{\small1}7|_{\small2}1|_{\small3}8|_{\small4}7|_{\small5}5|_{\small6}2|_{\small7}7|_{\small8}6|_{\small9}3}

The above are 10 single-digit numbers partitioned by 9 vertical bars 1 |_{{ }_1} through 9 . |_{{ }_9}. Our goal is to get a total sum of 1000 by removing some bars—1 bar, or 2 consecutive bars, as many times as you want—and thus creating some two-dight or three-digit numbers.

For example, if you decided to remove four bars 2 4 5 9 , |_{{ }_2}\ |_{{ }_4} |_{{ }_5}\ |_{{ }_9}, the sum would be 9 + 71 + 875 + 2 + 7 + 63. 9+71+875+2+7+63. And if you think this sum is indeed 1000, write your answer as 2459, the concatenation of the bar numbers from least to greatest.

What is your answer?


The answer is 14689.

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