# How Many Balls Are in the Bag?

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Puzzle Name

How Many Balls Are in the Bag?

Description of Puzzle solution

It is a problem about divisibility. According to the given instructions I must find what is the largest number that I can pick in the bag. The balls are numbered 1-99 but not all the numbers are used beacause the numbers that must be picked here is divisible by 6.

How the Solution was Found

Since, numbers are evenly divisible by 6 if they are evenly divisible by both 2 and 3 and I need to find the largest number in the bag that is divisible by 6. So I listed from numbers 1 - 99 that are divisible by 6

below is the list of numbers that are divisible by 6:

6                12              18               24

30              36              42              48

54              60              66               72

78               84             90               96

then I found out that there are 16 balls in the bag and the largest number is 96.

How interesting and challenging the puzzle was

The puzzle is very great, it will be easy for you if you just know the rules of divisibility of the numbers. I did it with so much fun.

Advice for Someone else working on the Puzzle

You must know the rules of divisibility to find the numbers that can be picked in the bag and you can use different strategies to find the numbers.

Find the How Many Balls Are in the Bag? puzzle on our puzzle hub.

TomLough
Hors connexion
Murray, Etats-Unis
Rôle: Équipe SEED
Inscription : 18/12/2009
Messages:

I understand this solution, but the other solutions are a little more difficult to understand, especially the one for 17 balls. That solution seems to start with a ball numbered with zero, but that does not seem to be allowed in the problem statement. Does anyone have any ideas about that?

IMarchenko
Hors connexion
Sugar Land, Etats-Unis
Rôle: Équipe SEED
Inscription : 02/05/2011
Messages:

Ha, that's a difficult one! Maybe because I have never been good with cominations.

I looked at the answers in the back of the book for this one and still had to take a few minutes to think it through in my head... Looks like there are also other soluntions available for this problem, but you've definitely started on the right track and got one of the solutions! Good job and Bravo!

Rolando Barcelon
Hors connexion
Quezon, Philippines
Rôle: Enseignant
Inscription : 08/01/2011
Messages:

Bravo maan!

Combinatorics helps explain the magic of life - the magic of combinations.

According to a popular saying, "Go to the world and multiply, not to subtract and divide."  But here, maan is getting fun to divide, keep it up maan!

Have fun!

God bless!