prove that the any restaurant bill of $n,n>or=5 be paid exactly using only $2 and $5 bills
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Expert's answer
2012-05-25T08:58:30-0400
Using an induction. Base: n=5$ it's okay. Claim: n=k statement is held. Check: n=k+1 k+1=k-5+6=k-5+2+2+2 (to pay this bill we used 1 5$ bill less and 3 2$ bills more, than before) If none 5$ bills were used, than k+1=k-4+5=k-2-2+5 (we use 2 2$ bills less and 1 5$ bill more)
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