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# Number Theory

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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 \$7\$ pieces of candy per scoop to the vat, and another machine that can remove exactly \$6\$ 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?

Jun 24, 2024

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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 \$7\$ pieces of candy per scoop to the vat, and another machine that can remove exactly \$6\$ 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?

Well, I say the least possible number number of times is 1 time.

Turn on both machines.  Machine 1 adds 7, and Machine 2 removes 6,

then real quick turn off both machines before they have time to cycle again.

Nobody said the machines have to keep running until all 1000 pieces are gone.

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Jun 24, 2024