Maths homework challenge :)

[Eater Sundae]

Junior is 7 so it took him quite a while to work through the ones that we had as his mental arithmatic is not brilliant:) Thanks for the extra 2.

 

The question doesn't ask for the formula, that is just me that wonders how you can work it it. I seem to remember needing to use factorials and the like when working out combinations. I know you guys like a little challenge every now and agin

 

Yes, they are quite interesting. I would imagine it's hard for most 7 year olds. Working out some of them is easy enough, but it would be hard for a 7 year old to do it methodically so they are confident that they had got them all.

[Lucy-Lastic]

Yes, they are quite interesting. I would imagine it's hard for most 7 year olds. Working out some of them is easy enough, but it would be hard for a 7 year old to do it methodically so they are confident that they had got them all.

 

This is what I thought too. I just talked to him about what facts do you already know (e.g. 9+6 = 15) and how he could use that and tried to get him to use some of the number bond information that he should (but doesn't) have (number bonds - what 2 numbers add together to make 10).

[Plain Talker]

Also, what age is Y3?

 

To convert age to "Y" you add 5. a Y3 child will be (5+3) ≈ 8

[Lucy-Lastic]

To convert age to "Y" you add 5. a Y3 child will be (5+3) ≈ 8

 

A Y3 child will be 7 to 8 (depending on when their birthday is). Junior will not be 8 until June, some in his class will not be 8 until the end of August.

[Plain Talker]

A Y3 child will be 7 to 8 (depending on when their birthday is). Junior will not be 8 until June, some in his class will not be 8 until the end of August.

 

Yeah, that's why I put that the child will be ≈ 8, same as a Y8 child will be ≈ 13

[onewheeldave]

You don't need 3 in each pile though, just 3 piles with each pile adding up to 15. I have got 7 ways so far.

 

9+6, 8+7, 5+4+3+2+1

9+5+1, 8+4+3, 7+6+2

9+4+2, 8+6+1, 3+7+5

9+3+2+1, 6+5+4, 8+7

8+5+2, 4+1+3+7, 9+6

6+4+3+2, 9+5+1, 8+7

6+5+3+1, 8+7, 9+4+2

 

From the question, I'd say that the piles do have to have 3 cards in them- if so, I'd knock out all the above that just have 2 numbers (or 4+).

 

Straight away the question makes me think of the 3x3 'magic square' (lo shu).

 

http://en.wikipedia.org/wiki/Magic_square#Lo_Shu_square_.283.C3.973_magic_square.29

 

That's the numbers 1-9 arranged in a square such that each horizontal column, vertical column and diagonals, add to 15 i.e.

 

8 1 6

3 5 7

4 9 2

 

which gives 8 combinations

 

(That's disregarding reflections and other variations of the same 3 numbers i.e. 159 is the same as 591)

[Eater Sundae]

From the question, I'd say that the piles do have to have 3 cards in them- if so, I'd knock out all the above that just have 2 numbers (or 4+).

 

Straight away the question makes me think of the 3x3 'magic square' (lo shu).

 

http://en.wikipedia.org/wiki/Magic_square#Lo_Shu_square_.283.C3.973_magic_square.29

 

That's the numbers 1-9 arranged in a square such that each horizontal column, vertical column and diagonals, add to 15 i.e.

 

8 1 6

3 5 7

4 9 2

 

which gives 8 combinations

 

(That's disregarding reflections and other variations of the same 3 numbers i.e. 159 is the same as 591)

 

If the question does require each pile to be 3 cards (which doesn't appear to be the case), then this is similar to my answer in post No 2, ie the 3 piles are the same as the 3 columns OR the 3 rows. ie there are 2 ways that the cards can be split.

 

If this is the case, then it feels more likely to be manageable as a formula, or consistent method of answering similar puzzles to work out how many answers there will be. Also, it feels more like a puzzle for a 7-8 year old. Are there any Sudoku fans out there who can help?

 

Edit. I've since started to read the link in onewheeldave's post, but had to give up for fear of my head exploding. It soon got way way beyond me.