An ATM machine only has two dollar bills not two onedollar b

An ATM machine only has two dollar bills (not two one-dollar bills) and five dollar bills. If you type in any number you want, and it will figure out how to divide things into the proper number of two’s and fives. Prove the ATM can generate any output amount greater than or equal to 4.

Solution

NUmbers larger than equal to 4 are of two forms

1. 4+2m ,m=0,1,2,3,4,...

Such numbers are generated using (m+2) ,2 dollar bills as : 4+2m=2(2+m)

2. 4+2m+1=5+2m, m=0,1,2,3,4,....

Such number are generated using, m 2-dollar bills and one 5-dollar bill.

So all amounts larger than equal to 4 can be generated.