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MathNet 2003 — Part 01 Question 40

Math Olympiad Vault · MathNet 2003 — Part 01

Question 40

A supermarket sells Rocacola and Rocajugo in bottles with lids. Additionally, exchange $15$ Rocacola caps for a full Rocajugo bottle, and exchange $20$ Rocajugo caps for a full Rocacola bottle.

Lucas has $511$ small caps that he exchanges at the supermarket for full bottles. After having the contents, you keep the lid, which you will use later to continue changing for full bottles. In the end he only has one cap of Rocacola left and none of Rocajugo. Determine how many Rocacola caps were among the $511$ initial caps. Of all the possibilities.