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Here's your next question (since null ruined the last one ;)).

What is the maximum number of pieces of pie you can have from slicing a pie 100 times? (The minimum is 101 pieces).

"If I die of a heart attack eating bacon, I'll be a happy man." -My father

What is the maximum number of pieces of pie you can have from slicing a pie 100 times? (The minimum is 101 pieces).

Based on a simple guess, I am going to say 396 pieces. This is based on the first cut being to slice the top and bottom of the pie in half, and then proceed in cutting normal halves with the remaining 99 slices.

You could slice the pie horizontally 50 times, and then vertically 50 times (placing most near the middle such that all slices intersect) creating a grid-like design. Even then, you would get 2601 slices, right?

1 slice placed horizontally and vertically would get you 4 slices.

2 slices placed horizontally and vertically would get you 9 slices.

3 slices would get 16. The pattern is squares.

So the formula is (n + 1)^2.

Hence, for 50 horizontal and vertical slices, you would get 51^2 or 2601 slices.

The actual number is higher than this, however. Try again! :D

"If I die of a heart attack eating bacon, I'll be a happy man." -My father

This post was edited by Hawkeye on Mar 16, 2006.

Wow I must be really a girl then. I have been trying to understand your reasoning for a while now, but I just don't get it. My math skills (and I did have them once) are definitely going down the drain. But I just cannot picture what you're saying Hawkeye.

However, when you say that 2 slices placed horizontally and vertically give you 9 slices... then do you have a predefinite position for the slices? Because I can think of a way you could have more than 9 slices in that way (of course, if my reasoning is right).

Un bacio è un'apostrofo rosa scritto tra le parole "ti amo".

Do they have to be even slices?

Look at me! I'm a prostitute robot from the future!

Do they have to be even slices?

I'm not sure if that's what you mean, but in case you're asking whether we can also cut curves instead of straight lines, I was about to ask the same.

Great minds think alike, I suppose :-)

"*sigh* Some men are really hard to manipulate!" - Orchid

This post was edited by null on Mar 17, 2006.

*Coughs*

not that i'd even think of cheating or anything...

There was that idea, but i was also asking if each slice had to be the same size and measurements.

Look at me! I'm a prostitute robot from the future!

You mean you'd be cunning enough to cut the cake like this?

(Assuming it's a rectangular chocolate cake on a pink table)

"*sigh* Some men are really hard to manipulate!" - Orchid

This post was edited by null on Mar 17, 2006.

Like the butler in that Adam Sandler movie, i am very very sneaky.

Look at me! I'm a prostitute robot from the future!

I believe that the answer in infinite.

If one where to make a spiral cut from the inside out. (This would work on a square pie as well.) Then 49 oscillating cuts across and 50 oscillating cuts down. I would then require the knowledge of the radius of the pie and the exact distance between you cuts. Also you will need to know the exact thickness of your cutting tool.

Awww, forget it just use a lazar and make each cut a molecules in width. How many molecules makeup the service of the pie? That is your answer, assuming you didn’t burn any with the lazar.

Suggestion:
Maybe you should ban the use of curves. Because me and my lasers have all the fun. : )

Thanks, ~ The Penguin Stalker ~ Im a pogramar... Iam a programer... I'm a programor...I write code.

I apologize. These presumptions are all valid, and it is my fault for not having defined them better.

The "pie" is circular, not square for starters.

A slice is to directly come down with a cutting knife once through the pie. In other words, it is a straight line which divides every piece it intersects with into two smaller pieces. Nothing is said for these two pieces, therefore they can be any shape and size.

Therefore, Bernie's diagraph would depict an accurate slicing of the pie, if it were in fact a circular chocolate pie with a pink table rather than a rectangular chocolate cake with a pink table.

By placing two slices vertically and two slices horizontally, you create a 3x3 grid of pieces. You can increase up to 50 by 50 vertical and horizontal slices (placed very close together so that some don't intersect outside the circular region).

But that isn't the right answer. You can have more than this.

"If I die of a heart attack eating bacon, I'll be a happy man." -My father

This post was edited by Hawkeye on Mar 17, 2006.

I believe that the answer in infinite.

The only thing I am fairly sure of is exactly that it cannot be infinite slices. I mean, I can see your point, but if you keep cutting the cake, at a certain point you'll have only crumbles left, and I don't think that is a valid premise.

However, if crumbles counted, my formula would count the fact that you can slice the cake 100 times horizontally, 100 times vertically, and you can repeat the process on the new slices. The problem would be, when would you stop? I mean, when will you be cutting only crumbles?

I am a bad mathematician, and therefore either I say infinite as our good fellow suggested, or I say "whoo let's get the guys on it" :P Afterall, when I was in high school I was not good with such problems either, and guys are known to be more knowledgeable than girls in maths.

Un bacio è un'apostrofo rosa scritto tra le parole "ti amo".

No, you only have 100 slices you can make. I just gave a for instance as 50 of those being horizontal and 50 being vertical, though you can slice it in any random way you wish. And afterwards the number of pieces made from that is what is important.

Also, you can't cut in 3 dimensions. This is not 3 dimentional pie! So no cutting from the sides or anything. Only from above.

"If I die of a heart attack eating bacon, I'll be a happy man." -My father

Since it seems you guys have given up, I will reveal the answer.

If we take a look at the pattern we get:

1 slice - 2
2 slices - 4
3 slices - 7
4 slices - 11
...
n slices - ?

The formula is (can be found without just looking, by counting line intersections):
Max_Pieces = 1 + 1 + 2 + 3 + ... + n
= 1 + n(n + 1)/2
= (n^2 + n + 2) / 2

Max_Pieces for 100 slices = (1002 + 100 + 2) / 2
= 10102 / 2
= 5051

"If I die of a heart attack eating bacon, I'll be a happy man." -My father

This post was edited by Hawkeye on Mar 20, 2006.