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You have a total supply of $1000$ pieces of candy, and an empty vat.  You also have a machine that can add exactly $5$ pieces of candy per scoop to the vat, and another machine that can remove exactly $3$ pieces of candy with a different scoop from the vat.  When these two machines are done, there is only one piece of candy left in the vat.  What is the smallest possible number of times the the first machine added candy to the vat?

 Jul 3, 2024
 #1
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If you let the first machine operate 2 times, it will have added 10 pieces,   

then you let the second machine operate 3 times, it will remove 9 pieces.   

This would leave 1 piece in the vat.   

.

 Jul 4, 2024

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