Sums of fours and fives

HardCombinatorics Brainteasers~7m

How many positive integers $\le 1000$ can be written as a sum of some $4$ s and/or $5$ s (using one or more terms)? For example, $21 = 4+4+4+4+5$ counts.

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Frobenius number of $\{4,5\}$ is $4\cdot5-4-5=11$ : every integer $\ge 12$ is representable.
Count $12..1000$ ( $989$ ) plus the representable values below $12$ ( $4,5,8,9,10$ ).

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994

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Asked at: Jane Street, Citadel

Sums of fours and fives

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