Exact change - ecomodder math riddle
 

We ecomodders like to fill our gas tanks consistently to full and generally avoid pumping extra gas to round to an exact dollar amount.

Now, most probably pay with credit cards and avoid change altogether. But I had this thought the other day:

Suppose you wanted to be prepared to give the cashier exact change, but of course you don't know what the exact cost will be. For this question, forget about paper dollars; we're only concerned about coins. What coin combination would you need to satisfy any change from 1 cent to 99 cents?

What is the fewest number of coins needed to satisfy this requirement, and what are those coins?

If I was more familiar with the Euro I would try to find the Euro equivalent for this question, but I don't know too much about the increments across the pond!

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Ten coins (not using fifty-cent pieces): four pennies, two nickels, one dime, three quarters; nine coins if a fifty-cent piece replaces two of the quarters.



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In New Zealand you'd need 1 10c, 2 20c, 1 50c (10c is the smallest). And if you wanted to have it for up to $5 (smallest bill), you would also need 2 $2 coins and a $1 coin.

I'd just use one of my adjustable coins that let me set the value from 1c to 99c with a little knob.

I have to be honest here. You beat me.

For some reason, I was set on using 2 quarters instead of 3 (resulting in extra dimes). Well done. The 50 cent piece was a nice surprise.

...all the above is negated (but certainly NOT improved upon) by use of appropriate plastic.

how about sitting in the parking lot and taking a few minutes to calculate the price, then go in and prepay(plus a dollar to ensure you fill the tank), and see how close you come? that could be fun, especially if you tell the cashier you'll get a dollar in change and you're correct

One (1) coin and no change: Pay with a silver dollar and drop the change in the "Tips" jar.

Not as good as jakobnev, though;)

I dont know about anybody else, but i generally know when ill have to fill up with fuel before i set off (ie: about 1/4 tank left) so i quickly check how much change - in coins / notes - i have. When i fill up, i dont go over the amount i have in change. Simple.