Pizza

Number Theory Level 1

15 friends are trying to share a pizza that has been cut into 10 equal slices.

There is no way to evenly split 10 slices among 15 people, so they again cut each slice into 10 equal pieces. But there is still no way to evenly split 100 equal pieces among 15 people.

If they keep cutting each slice into 10 equal pieces like this, will they eventually be able to split the pizza equally?

Yes No

Christopher Boo by Christopher Boo , 24, Singapore

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3 solutions

Ayush Kumar
Oct 13, 2017

By dividing repeadetly into tens, you will get all the powers of 10. 15 has a factor of 3 that multipying by 10 will never get. Therefore, it will n o t \boxed{not} be possible to ever divide the pieces evenly.

7 Helpful 0 Interesting 0 Brilliant 0 Confused
Azadali Jivani
Oct 14, 2017

1/15 = 0.0666666..........
10/15 = 0.666666...........
100/15 = 6.666666........
and its so on. that's why it's not possible


2 Helpful 0 Interesting 0 Brilliant 0 Confused

That's an interesting way to put your solution. I have to say, it's definitely more simple than mine.

Slendy Slender - 3 years, 7 months ago
Slendy Slender
Nov 8, 2017

As long as the number is divisible by ten and divided by ten, then equals ten, the number is not divisible by fifteen. Every time we multiply by ten (dividing each slice into ten peices multiplies the number of slices by ten), we get a number that meets the set requirements, and therefore not divisible by fifteen.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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