Stella’s Bookshelves

As we all know, Stella studied piano with the renowned Nadia Boulanger in Paris after World War II. In Amsterdam, in her studio, she has three shelves with books of four-hand piano music that she often plays with her husband Graziano (who needs to practice more). The top shelf contains 1/6 of all the scores. The middle shelf contains more than 2/5 of the scores, and the bottom shelf contains only four scores (but they’re thick ones). What is the smallest total number of scores that she might have on all three shelves?


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The total number of scores, x, is a multiple of 6.
The top and bottom shelves contain less than 3/5 of the total:

So x could be 12. Then:

Stella wishes Graziano would practice more, but she doesn’t want to nag.

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