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**misbas****Member**- Registered: 2010-11-27
- Posts: 1

How to explain the following problem

A group of more than 12 singers, but less than 32, sometime they sing in pairs of 3, 4 and 6 - how many singers are there altogether? I am trying explain to my son who is 6

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,517

Hi misbas;

First, understand this is a fairly difficult problem for a six year old. Most adults will be unable to do it also.

Start him off as thinking about it in terms of sets or collections of objects.

This is all the numbers that are greater than 12 but less than 32

{13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31}

That is all the possible answers. Obviously some of them are wrong but we have narrowed it down to 19 different numbers of guys in the band.

For them to play in groups of three the number has to be divisible by 3. 5 guys in the band cannot play in groups of 3. Why? Take away the first group of 3 and you have 2 left over that is not a group of 3. Now 6 guys can play as 2 groups of 3. We go through all the possibilites and pick out only the numbers of guys that also form groups of 3. We get

{15,18,21,24,27,30,33}

Look at that group above. Each number, say 18 guys can play in groups of 3. Prove that that by actually making the groups of 3. You will see that it forms 6 perfect groups of 3. So we now only have 7 possiblities (the ones above)

For them to play in groups of four the number has to be divisible by 4. 18 guys in the band cannot play in groups of 4. Why? Take away the first group of 4 and you have 14 left over

Take away the second group of 4 and you 10 left. Take away the next group of 4 and you have 6. Now take away the next and you have 2 left over. Now 8 guys can play as 2 groups of 4. We go through all the possibilites and pick out only the numbers of guys that also form groups of 4. We get

{24}

We are down to one number. One last test too. Can 24 form groups of 6? Yes it can 6, 6 , 6 , 6. 4 perfect groups of 6. You are done, 24 is the answer.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**Lance Caelan****Member**- Registered: 2010-12-27
- Posts: 2

Here are some problems for maths geniuses

1. Catie placed the numbers 1 to 5 in the squares of the letter C, so the sum of the 2 numbers in the top row was the same as the sum of the two numbers in the bottom row, and the same as the sum of the three no. in the column. Show every possible way Catie could've placed the numbers and explain why there are no more solutions.

_____

|__|__|

|__|__

|__|__|

2. Mary's photocopier has seven buttons letting her reduce or enlarge the area of a printed image:

50%,75%,80%,100%,120%,125%,150%

a) Mary wants to enlarge a picture. She does not want to copy more than 3 times. What is the closet she can get to an enlargement of 200%

b) Using just 4 of its 7 buttons and making copies of copies of necessary, Mary's phtocopier can produce the same size images as the complete set of seven buttons. Find 2 sets of 4 buttons with this property.

___________________

Homework help

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,517

Looking now I see that 2 of these questions are all over the internet. They have been answered many times already.

So these are hardly for geniuses, all anyone would have to do is just look up the answer. I know that is no fun but it is a possibility.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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