A pizza is cut with a knife. There are 7 straight cuts that are made. The maximum number of pieces that can be obtained from the pizza (not necessarily of equal sizes) is?

Dear Speed,

 when there is 1 cut there would be   2 pieces

when there are 2 cuts the maximum number of pieces you get when the two lines intersects so we will get 4 pieces 

and when there 3rd cut then it should cut the 2 lines and we will get  6 pieces

and when there 4th cut then it should cut the 3 lines and we will get  8 pieces

 so we see that there is a pattern 2(n-1) + 2 are the maximum number of pieces and n is the number of cuts

so we 7 cuts put n= 7

so we get maximum number of pieces are 14 

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jitender

Hi Speed Racer,

To get the maximum number of pieces, each cut should overlap all the previous cuts that were already made on the pizza.

So after 1st cut ------- 2 pieces.

after second cut ------- 4 pieces = 2+2

after 3rd cut ------- 7 pieces = 4+3

after 4th cut ------- 11 pieces = 7+4

Similarly proceeding, after the 7th cut you can have a maximum of 29 pieces.

Hope this helps.

Best Regards,

Ashwin (IIT Madras).

mr.ashwin

i did not understand how each cut will overlap previous cut practically and also what question means exactly

please please explain

Suchita,

Here suppose 1 cut is made, we will have two pieces.

Now suppose the 2nd cut is made parallel to the first cut on the pizza, then we will have only 3 pieces after 2 cuts.

But say suppose we make two cuts, such that the two cuts pass through the centre then we will have 4 pieces. So we can see that the maximum number of pieces can only be obtained when the next cut made intersect the other cuts made.

Now that the third cut must intersect the previous two cuts made, not at the point of intersection of the 1st two cuts, but in two points that distinctly.

ie the third cut must intersect the 1st and the 2nd cut at two different points, so that the maximum number of pieces is obtained.

So that after the 3rd cut we can have a maximum of 7 pieces.

And keep proceeding in that manner.

Hope it helps.

Regards,

Ashwin (IIT MadraS).

thanks now its clear