Patrick's Pizza Party Puzzle

Logic Level 4

Patrick's pizza party will have either 7 or 8 guests. What is the fewest number of pieces he could pre-cut his pizza into to ensure that each guest can take an equal amount of pizza without any additional cuts and with no pizza left over?

Note: The slices do not need to be the same size.


The answer is 14.

Eli Ross by Eli Ross

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5 solutions

Eli Ross Staff
Sep 14, 2015

To satisfy 8 people, we first cut the pizza into 8 equal slices. When 7 people arrive, we have 1 slice left over! Thus, we cut the 8th equal slice into 7 equal slices (in advance), for a total of 14 slices in total (7 big slices and 7 little slices). So, if 7 people come each of them take 1 big and 1 little slice, and if 8 people come, 7 of them get 1 big slice, and one of them gets all of the little slices.

It is possible to show that it cannot be done in fewer slices. Can someone explain why?

14 Helpful 0 Interesting 0 Brilliant 0 Confused

If the 8th guest gets all the smaller slices then all the guests donot get equal 'amount' of pizza.

Zainab Rahman - 5 years, 9 months ago

You can do 8 equal slices, let's supose we are made 8 sectors of a circle?How do you get to make seven equals slices in a sector of a circle of 45 degrees?Can you explain me this geometrically?or, if the slices are not sectors, what are the shape of the slices?... Actually, if I can do it this like you,I can do it with 9 cuts at most. how can I do it? I make one slice( a sector of the pizza) (I cut twice to make the sector) of area 1/56 of the area of the circle and then if for example there are 8 people I overlay my slice 7 times above the pizza and I make 1 cut and I keep on like this with the rest... I'll make 9 cuts. If seven people is coming I overlay my slice 8 times above the pizza and I cut and I keep on like this... I'll make 8 cuts

Guillermo Templado - 5 years, 8 months ago

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Why don't we just keep it simple. Cut the pizza in 8 slices. The slices may not be equal as is mentioned in the question. If 7 guests come you eat the 8th yourself and if 8 come you don't eat rhe pizza. Cutting one big piece into 7 smaller pieces would mean that if 7 guests arrive then 7 would get 1 slice and one of them would get 7 slices regardless of the size.

Zainab Rahman - 5 years, 8 months ago

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They have to get the same amount of pizza

Guillermo Templado - 5 years, 8 months ago

I'd like to point out that it said "each guest can take an equal amount of pizza without any additional cuts and with no pizza left over" so if we cut it into 8 pieces and 7 show up we get one or if 8 show up nothing will happen

Ken Falken - 3 months ago

What if you cut the pizza in 8 slices. If 8 guests arrive then give one to each and if 7 guests arrive you eat the 8th one yourself. In this way the pizza will be equally distributed with no left overs.

Zainab Rahman - 5 years, 9 months ago

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Now, this is logic plus common sense.

Kamalyesh Kannadkar - 5 years, 9 months ago

Awesome thinking! I got confused in this. :D

Abubakar Sargana - 5 years, 9 months ago
Kelvin Lau
Sep 17, 2015

5 Helpful 0 Interesting 0 Brilliant 0 Confused
Ivan Koswara
Sep 16, 2015

It's easy to obtain a solution with 14 pieces: cut seven pieces 1/8 and seven pieces 1/56. If 7 guests arrive, take one big (1/8) and one small (1/56) piece; if 8 guests arrive, seven people take one big piece each and one person takes all small pieces.

It's also easy to see that 14 is necessary: all pieces can't be bigger than 1/8 (since, if 8 people arrive, each person gets at least one slice and exactly 1/8 of the pizza, so all slices aren't larger than 1/8). This implies if 7 guests arrive, all pieces are too small; every guest must receive at least two pieces, for a total of 14.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Its not possible to do less than 14, because whatever you end up having has to be a multiple of 7 (in the best case). The highest multiple of 7 less than 14 is 7, and for 8 people (which is the worst case), that is not good enough.

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Achille 'Gilles'
Sep 16, 2015

14 pieces,

First, make 8 stardard pieces then cut one of those in 7 pieces so a total of 7 big and 7 small pieces therefore 14 pieces.

1 full pieces for each of the 8 persons or

1 large and 1 small pieces for each of the 7 persons.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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