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Prove by induction that all coins greater than or equal to 8 pence can be made using 3 pence and 5 pence coins . Here is my thought : I looked at Z+ greater than 8 ... I considered multiples of 3(equivalent to using 3p coins with repetitions) and considered multiples of 5. Rest of them were mostly primes where I had to combine both 3 and 5 . And I noticed that 3 and 5 are in the form of 4k+1 and 4k-1.

I would appreciate any information . Thanks

hmakholm left over Monica
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Abu Bardewa
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2 Answers2

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If you can make $8,9,10$, then you can add enough $3$'s to one of them to make any higher number.

Ross Millikan
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  • That makes sense . But I wanted to see with notations because I want to be familiar with the kind of notations and symbols used for proofs. – Abu Bardewa Nov 20 '15 at 21:30
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There is a theorem called the chicken mcnugget theorem that says: the largest integer that is not a combination of m and n is mn - (m+n). The proof can be found easily online.

Yunus Syed
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