<p>In the state of Coinland, coins have values <img alt="$6,10,$" height="17" src="https://latex.artofproblemsolving.com/a/8/6/a8632de9fb4f25dd923e67887531a94f8b44477b.png" width="42" /> and <img alt="$15$" height="13" src="https://latex.artofproblemsolving.com/f/1/9/f1965fae079a9ba2c0726c307070c2355dfcb213.png" width="17" /> cents. Suppose <img alt="$x$" height="10" src="https://latex.artofproblemsolving.com/2/6/e/26eeb5258ca5099acf8fe96b2a1049c48c89a5e6.png" width="12" /> is the value in cents of the most expensive item in Coinland that cannot be purchased using these coins with exact change. What is the sum of the digits of <img alt="$x?$" height="12" src="https://latex.artofproblemsolving.com/d/c/f/dcf0e6ce51321975abd84e55dc4cee47dec1a4db.png" width="18" /></p>

Question No: 349

In the state of Coinland, coins have values $6,10,$ and $15$ cents. Suppose $x$ is the value in cents of the most expensive item in Coinland that cannot be purchased using these coins with exact change. What is the sum of the digits of $x?$

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Tags: Algebra Combinatorics

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