## Tuesday, October 20, 2009

Imagine you are an empress or emperor of a new kingdom and you need to introduce a new currency named Shlumpies. You call your Minister of Finance and ask her to design paper bills for Shlumpies. What is the minimal number of different denominations that you need to design, if you want to be able to pay any number of Shlumpies (up to a 100) using no more than three bills of each type?

For example, in the US kingdom we have \$1, \$2, \$5, \$10, \$20, \$50 bills. You can pay any dollar amount (up to a \$100) using up to three bills of each type. Your kingdom is trying to be superior, managing with less types of bills. Can you do it?

Submit your answer on our Family Puzzle Marathon site. Solve three puzzles and get a prize!

Kim said...

I think you need 4 types.

If you had, for example: \$1, \$3, \$10 and \$40 bills that ought to do it.

Kim said...

Sorry, not \$, those were supposed to be in Shlumpies! :-)

prluhmann said...

I think the answer is 4 bills, but a more efficient answer than Kim's is 1,4,16 and 64

Maria said...

She did it again beating all the West-coasters and late raisers! We indeed should be able to manage with four types of bills and proposed by Kim 1, 3, 10 and 40 would allow to make any number between 1 and 100. Another point for Kim.

I also like prluhmann solution. It is indeed more efficient as we will also be able to make up any number up to 255 using no more than three of each bill type. I think prluhmann also deserves a point with his/her brave swift entry into our puzzle marathon and an alternative efficient solution.

New puzzle tomorrow!

Kim said...

I knew 4 Shlumpy bills would be better than 3, but I just couldn't see myself paying with them... :-)

Anonymous said...

how do you get to 49 with prluhmann's answer using no more than 3 bills of each type?

I think Kim's answer is best

Maria said...

To get to 49, you will use three bills of 16 and one bill of 1 shlumpies. I wonder whether there is any country that has a 4 and 16 currency bills...

Anonymous said...

3 16's is 48, add 1 shlumpy to get 49 easy peazy lemon squezzy

Anonymous said...

1,2,7 and 30 also holds good

Anonymous said...

The only proper "denomination" would be a prime number and therefore indivisible. 1,3,13,37 is the set that fits this bill.

Unknown said...

or 1,3,13,51

Unknown said...

oops 1,3,13,47 51 aint prime forgot my 17's table.