I Love Pizza

Probability Level 2

A pizza can be cut into maximum 2 parts by a single cut

A pizza can be cut into maximum 4 parts by 2 cuts.

A pizza can be cut into maximum 7 parts by 3 cuts

Find the maximum no. of parts in which a pizza could be cut using 10 cuts.

Note : The cuts can be unequal


The answer is 56.

Anirudha Brahma by Anirudha Brahma , 19, India

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1 solution

Anirudha Brahma
Apr 6, 2016

Note : This is the way i had done this problem

No of parts in 0 cuts = 0 (+1)

No of parts in 1 cuts = 1 (+1)

No of parts in 2 cuts = 1 + 2 (+1)

No of parts in 3 cuts = 1 + 2 + 3 (+1)

Observation No. of parts in n cuts = sum of first n integers + 1

In this way No of parts in 10 cuts = 1+2+3+4+5+6+7+8+9+10(+1)

= 56

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Can you explain the generalisation? I didn't get it. Thanks in advance! :-)

Aniruddha Bhattacharjee - 5 years, 2 months ago

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What we realised from the pattern is that if we do n no. Of cuts then the Maximum no. Of parts we get are is the sum of first n numbers starting from 1 and ending on n and then we add an extra 1 according to the pattern

Do not hesitate to ask again if you did not understand

Anirudha Brahma - 5 years, 2 months ago

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Got it! Thanks! :-)

By the way, can this be proved using induction?

Aniruddha Bhattacharjee - 5 years, 2 months ago

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