Is this necessary, sufficient or both?Gavin Chipper wrote:OK, so the lowest value for the next coin up is double the previous value minus one. And the highest system breaker is the (previous one minus one) squared. All assuming there is a 1 in the system. But it's easily fiddled with.Charlie Reams wrote:Ties definitely are allowed.
Making Change
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Re: Making Change
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Actually I was wrong. The lowest value for the next coin up is double the previous one minus the next one down from that. So if you had 1, 10, 19 then the lowest value for the next one would be 19*2-10=28.Charlie Reams wrote:Is this necessary, sufficient or both?Gavin Chipper wrote:OK, so the lowest value for the next coin up is double the previous value minus one. And the highest system breaker is the (previous one minus one) squared. All assuming there is a 1 in the system. But it's easily fiddled with.Charlie Reams wrote:Ties definitely are allowed.
Also if you start with something other than a 1, then every value would have to be a multiple of the initial value, so you can still use the same system to find the lowest next value or highest system breaker by dividing everything by the lowest value, doing the thing, and multiplying up again.
Is what necessary, sufficient or both? About starting with the 1? Hopefully I've answered it if it is.
Re: Making Change
If we had coins thats values were only powers of two, the most efficient way to get any value of money would always give an assortment of coins in which none were repeated.