Fun with Pies

You have 9 round pies. There are 10 people at your party. Your task is to divide the 9 pies such that all 10 people get the same amount of pie, everyone has the same number of slices of pie, and there is none left over.

The challenge is to use the least amount of pie slices. And no, the answer is not cut the 9 pies into 10 pieces each for a total of 90 slices and give each person 9 slices.

Find the least amount of slices per person to divide all 9 pies equally among 10 people.

Good Luck. (reworded for better clarity)

What constitutes a cut? For example does cutting each of the 10 pies into a 1/10 and 9/10 split count as only 10 cuts? If so then this must be the answer as certainly every pie has to be cut at least once.

Originally posted by Zuggy
What constitutes a cut? For example does cutting each of the 10 pies into a 1/10 and 9/10 split count as only 10 cuts? If so then this must be the answer as certainly every pie has to be cut at least once.

see revised wording

Hmm. Nobody can get a whole pie - that would be too much.
So each pie must have a piece cut out.

You can cut a piece off the edge with one cut

So, with ten cuts, cut a piece equal to a tenth of the pie off each pie. If you are allowed to stack the pies you can do it with one cut, otherwise it is 9 cuts. Nine people get a large piece, 9/10ths of a pie big, and one person gets 9 small pieces each 1/10th of a pie big.

anyone want to calculate where the cut must be made?

Originally posted by uzless
You have 9 round pies. There are 10 people at your party. Your task is to divide the 9 pies such that all 10 people get the same amount of pie, everyone has the same number of slices of pie, and there is none left over.

The challenge is to use the least amount of pie slices. And no, the answer is not cut the 9 pies into 10 pieces each for a total of 90 ...[text shortened]... erson to divide all 9 pies equally among 10 people.

Good Luck. (reworded for better clarity)

So slice off 85% of the first pie and give it to person 1. (We'll come back to him later.)

The remaining 15% of pie 1 goes to person 2, along with 75% of pie 2, etc., giving:

85
15/75
25/65
35/55
45/45
55/35
65/25
75/15
85/5
95

Give the last guy's 5% to person 1, and cut the rest of the last guy's pie into 2 slices of any size to satisfy the requirement that all people must have the same # of slices.

This is 2 slices per person. Can it be further optimized?!

Originally posted by BigDoggProblem
So slice off 85% of the first pie and give it to person 1. (We'll come back to him later.)

The remaining 15% of pie 1 goes to person 2, along with 75% of pie 2, etc., giving:

85
15/75
25/65
35/55
45/45
55/35
65/25
75/15
85/5
95

Give the last guy's 5% to person 1, and cut the rest of the last guy's pie into 2 slices of any size to ...[text shortened]... le must have the same # of slices.

This is 2 slices per person. Can it be further optimized?!

Ah, I missed the bit about the same number of slices each.

Using your cunning recipe, couldn't each "slice" be a circular segment?
http://en.wikipedia.org/wiki/Circular_segment

That gives 2 pieces per person with only 10 cuts. I don't think that can be bettered, as each pie needs a bit cut off, so that is at least 9 cuts, and if we give 9 people 90% with 1 cut, then we have taken 9 cuts (the minimum) but the last guy gets too many bits.

Originally posted by iamatiger
Ah, I missed the bit about the same number of slices each.

Using your cunning recipe, couldn't each "slice" be a circular segment?
http://en.wikipedia.org/wiki/Circular_segment

That gives 2 pieces per person with only 10 cuts. I don't think that can be bettered, as each pie needs a bit cut off, so that is at least 9 cuts, and if we give 9 people 90% with 1 cut, then we have taken 9 cuts (the minimum) but the last guy gets too many bits.

Yes, circular segments, which get to the correct percentage with only 1 cut.