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In my country i decided to develop my own currency. Long tired of the decimal system, i decided to arbitrarily make a new currency system. From now on 121 coins make 1 Bmad bill. $121 one BMAD bills makes a hundred and so on. Also, i decided that All numbers within each system must be reached by no more than five bills/coins. In other words. If i want 119 cents, then five coins or less must be enough to reach that amount. If i want 120 cents, then i would use at most five coins too but it does not have to be the same five coins that made 119. So to reach any price amount under a hundred, i would need at most five bills and five coins.

Three questions:

1. What is the fewest number of coins needed to make the above true? What would be their values?

2. How many one BMAD bills are needed to make a million?

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2.

121 coins = 1 dollar

14641 coins = 121 dollar = 1 hundred bill

1771561 coins = 14641 dollar = 121 hundred = 1 ten-thousand

214358881 coins = 1771561 dollar = 14641 hundred = 121 ten-thousand = 1 million

That sound right?

The fewest number of coins is 5. There are several sets of 5 values which work.

One set is {1,4,9,31,51}.

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2.

121 coins = 1 dollar

14641 coins = 121 dollar = 1 hundred bill

1771561 coins = 14641 dollar = 121 hundred = 1 ten-thousand

214358881 coins = 1771561 dollar = 14641 hundred = 121 ten-thousand = 1 million

That sound right?

Edited by bonanova
add spoiler

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The fewest number of coins is 5. There are several sets of 5 values which work.

One set is {1,4,9,31,51}.

How would you make 30?

9+9+9+1+1 = 29

9+9+9+4 = 31

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The fewest number of coins is 5. There are several sets of 5 values which work.

One set is {1,4,9,31,51}.

How would you make 30?

9+9+9+1+1 = 29

9+9+9+4 = 31

9+9+4+4+4

Edited by fabpig

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