BdMO National Primary 2016#5

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
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samiul_samin
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BdMO National Primary 2016#5

Unread post by samiul_samin » Wed Feb 20, 2019 11:44 pm

There are $7$ violet balls, $6$ blue balls, $5$ ndigo balls, $4$ green balls, $3$ yellow balls, $2$ orange balls and $1$ red ball. They should be kept at minimum number of boxes in such a way that no box contains more than one ball of same color and each box contains same number of balls. What is the number of balls in each box?

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samiul_samin
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Re: BdMO National Primary 2016#5

Unread post by samiul_samin » Fri Feb 22, 2019 11:18 am

Hint
Pigeonhole Principle
Answer
$4$
Solution
There are $7$ Violet balls.So we need at least $7$ boxes.
Total ball $=1+2+3+4+5+6+7=28$
So,$\dfrac {ball}{box}=\dfrac {28}{7}=4$
$4$ balls in each box.

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