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SMO 2015 Junior Round 1 Question 32

SMO · SMO 2015 Junior Round 1

Question 32

A donut shop sells its donuts only in packs of 6 (half-dozen) or in packs of 13 (a baker's dozen). So it is impossible to purchase exactly 14 donuts from this shop, since 14 cannot be written as an integral combination of 6 and 13. Find the largest number of donuts that cannot be purchased from this shop.