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MathNet 2018-part-06 — 181 problems (EN–VI) Question 115

Math Olympiad Vault · MathNet 2018-part-06 — 181 problems (EN–VI)

Question 115

It is given that the bookshelf can fit $9$ of the same thick books, but the $10$th one will not fit anymore. Similarly, it can hold $15$ of the same thin books, but $16$th will not fit anymore. Is it possible for that shelf to hold simultaneously:

a) $6$ thick and $5$ thin books?

b) $7$ thick and $5$ thin books?