Combination question

[Peter T]

This is shameless I know, but I'm stuck with my daughter's homework
question. Here's the question -

"Nine eggs numbered 1 to 9. Put the nine eggs into three baskets. The total
of the numbers on the eggs in each basket must be the same. How many
different ways are there to do it?"

As it's not stated to the contrary, I assume each basket can contain any
number of eggs, though each basket must contain at least one egg and hence a
maximum of seven eggs.

No doubt can be solved with VBA, but here's the rub - this is for a twelve
year! There's got to be a catch ?

Anyone interested in a virtual merit...

Regards,
Peter T

 

[Guest]

4

 

[Bernard Liengme]

Peter,
Not to be a grump on such a sunny day (in Nova Scotia) but you are depriving
daughter of a chance of discovering the fun of math! Let her look at this
and see if she can find more. Give her 9 pieces of paper with digits 1 thru
9, and three plates. Then go play golf.

sum Any three of these ways
5 5 4+1 2+3 1
6 6 5+1 4+2 1
7 7 6+1 5+2 4+3 4
8 8 7+1 6+2 5+3 4
9 9 8+1 7+2 6+3 5+4 10
10 9+1 8+2 6+4 1
10 9+1 6+4 5+3+2 1
11 9+2 8+3 7+4 6+5 4
12 9+3 8+4 7+5 6+4+2 4
13 9+4 8+5 7+6 7+3+2+1 4
14 9+5 8+6 7+4+3 7+4+2+1 4
15 9+6 8+7 1+2+3+4+5 1

best wishes

 

[Peter T]

Thanks, Bernard,

Previously shameless, now shamed! On all counts, abuse of the group,
depriving my daughter of the 'fun of maths', and (worryingly) not seeing the
obvious.

Well, it's been a beautiful sunny and unseasonably warm day here too (in the
UK). I'll blame my aberration on that, too much golf, and global warming!

Thanks also Gary''s Student.

Regards,
Peter T

 

[Dana DeLouis]

Hmmm. They all sum to 15.

Select[KSetPartitions[r,3], Equal@@Total/@#1 &]

{{1,5,9},{2,6,7},{3,4,8}},
{{1,5,9},{2,3,4,6},{7,8}},
{{1,6,8},{2,4,9},{3,5,7}},
{{1,2,3,9},{4,5,6},{7,8}},
{{1,2,4,8},{3,5,7},{6,9}},
{{1,2,5,7},{3,4,8},{6,9}},
{{1,3,4,7},{2,5,8},{6,9}},
{{1,3,5,6},{2,4,9},{7,8}},
{{1,2,3,4,5},{6,9},{7,8}}

(Math Program)

 

[Peter T]

She got the 15's with Bernard's approach, but only six of them. A small
correction to be done before it's handed in in the morning, thanks to you!

I wonder if there's not another way to get that solution without resort to
bits of paper on plates, 'Math Program' or VBA. It's back to school for me I
think <g>

Regards,
Peter T

PS to Bernard

I showed your reply to my daughter, this bit -
"a chance of discovering the fun of math!"
- got a very loud "huh" !

Hmmm. They all sum to 15.

Select[KSetPartitions[r,3], Equal@@Total/@#1 &]

{{1,5,9},{2,6,7},{3,4,8}},
{{1,5,9},{2,3,4,6},{7,8}},
{{1,6,8},{2,4,9},{3,5,7}},
{{1,2,3,9},{4,5,6},{7,8}},
{{1,2,4,8},{3,5,7},{6,9}},
{{1,2,5,7},{3,4,8},{6,9}},
{{1,3,4,7},{2,5,8},{6,9}},
{{1,3,5,6},{2,4,9},{7,8}},
{{1,2,3,4,5},{6,9},{7,8}}

(Math Program)
--
Dana DeLouis

Peter,
Not to be a grump on such a sunny day (in Nova Scotia) but you are
depriving daughter of a chance of discovering the fun of math! Let her
look at this and see if she can find more. Give her 9 pieces of paper with
digits 1 thru 9, and three plates. Then go play golf.

sum Any three of these ways
5 5 4+1 2+3 1
6 6 5+1 4+2 1
7 7 6+1 5+2 4+3 4
8 8 7+1 6+2 5+3 4
9 9 8+1 7+2 6+3 5+4 10
10 9+1 8+2 6+4 1
10 9+1 6+4 5+3+2 1
11 9+2 8+3 7+4 6+5 4
12 9+3 8+4 7+5 6+4+2 4
13 9+4 8+5 7+6 7+3+2+1 4
14 9+5 8+6 7+4+3 7+4+2+1 4
15 9+6 8+7 1+2+3+4+5 1

best wishes

 

[Dana DeLouis]

I wonder if there's not another way to get that solution

If you want the total # of solutions in order to check an algorithm,
then under //Check in both programs pulled up A112972

http://www.research.att.com/~njas/sequences/A112972

ie when n=9, there should be 9 solutions.
--
HTH :>)
Dana DeLouis
Windows XP & Office 2007

She got the 15's with Bernard's approach, but only six of them. A small
correction to be done before it's handed in in the morning, thanks to you!

I wonder if there's not another way to get that solution without resort to
bits of paper on plates, 'Math Program' or VBA. It's back to school for me
I
think <g>

Regards,
Peter T

PS to Bernard

I showed your reply to my daughter, this bit -
"a chance of discovering the fun of math!"
- got a very loud "huh" !

Hmmm. They all sum to 15.

Select[KSetPartitions[r,3], Equal@@Total/@#1 &]

{{1,5,9},{2,6,7},{3,4,8}},
{{1,5,9},{2,3,4,6},{7,8}},
{{1,6,8},{2,4,9},{3,5,7}},
{{1,2,3,9},{4,5,6},{7,8}},
{{1,2,4,8},{3,5,7},{6,9}},
{{1,2,5,7},{3,4,8},{6,9}},
{{1,3,4,7},{2,5,8},{6,9}},
{{1,3,5,6},{2,4,9},{7,8}},
{{1,2,3,4,5},{6,9},{7,8}}

(Math Program)
--
Dana DeLouis

Peter,
Not to be a grump on such a sunny day (in Nova Scotia) but you are
depriving daughter of a chance of discovering the fun of math! Let her
look at this and see if she can find more. Give her 9 pieces of paper with
digits 1 thru 9, and three plates. Then go play golf.

sum Any three of these ways
5 5 4+1 2+3 1
6 6 5+1 4+2 1
7 7 6+1 5+2 4+3 4
8 8 7+1 6+2 5+3 4
9 9 8+1 7+2 6+3 5+4 10
10 9+1 8+2 6+4 1
10 9+1 6+4 5+3+2 1
11 9+2 8+3 7+4 6+5 4
12 9+3 8+4 7+5 6+4+2 4
13 9+4 8+5 7+6 7+3+2+1 4
14 9+5 8+6 7+4+3 7+4+2+1 4
15 9+6 8+7 1+2+3+4+5 1

best wishes
--
Bernard V Liengme
www.stfx.ca/people/bliengme
remove caps from email

This is shameless I know, but I'm stuck with my daughter's homework
question. Here's the question -

"Nine eggs numbered 1 to 9. Put the nine eggs into three baskets. The
total
of the numbers on the eggs in each basket must be the same. How many
different ways are there to do it?"

As it's not stated to the contrary, I assume each basket can contain any
number of eggs, though each basket must contain at least one egg and
hence a
maximum of seven eggs.

No doubt can be solved with VBA, but here's the rub - this is for a
twelve
year! There's got to be a catch ?

Anyone interested in a virtual merit...

Regards,
Peter T

 

[Peter T]

Hi Dana,

An interesting link, thanks.

From what I gather quite a few dad's got roped into helping with this one!

FWIW, the other related homework questions had 'think out of the box' type
solutions which, perversely, threw me on this one!

Regards,
Peter T

I wonder if there's not another way to get that solution

If you want the total # of solutions in order to check an algorithm,
then under //Check in both programs pulled up A112972

http://www.research.att.com/~njas/sequences/A112972

ie when n=9, there should be 9 solutions.
--
HTH :>)
Dana DeLouis
Windows XP & Office 2007

She got the 15's with Bernard's approach, but only six of them. A small
correction to be done before it's handed in in the morning, thanks to you!

I wonder if there's not another way to get that solution without resort to
bits of paper on plates, 'Math Program' or VBA. It's back to school for me
I
think <g>

Regards,
Peter T

PS to Bernard

I showed your reply to my daughter, this bit -
"a chance of discovering the fun of math!"
- got a very loud "huh" !

Hmmm. They all sum to 15.

Select[KSetPartitions[r,3], Equal@@Total/@#1 &]

{{1,5,9},{2,6,7},{3,4,8}},
{{1,5,9},{2,3,4,6},{7,8}},
{{1,6,8},{2,4,9},{3,5,7}},
{{1,2,3,9},{4,5,6},{7,8}},
{{1,2,4,8},{3,5,7},{6,9}},
{{1,2,5,7},{3,4,8},{6,9}},
{{1,3,4,7},{2,5,8},{6,9}},
{{1,3,5,6},{2,4,9},{7,8}},
{{1,2,3,4,5},{6,9},{7,8}}

(Math Program)
--
Dana DeLouis

Peter,
Not to be a grump on such a sunny day (in Nova Scotia) but you are
depriving daughter of a chance of discovering the fun of math! Let her
look at this and see if she can find more. Give her 9 pieces of paper with
digits 1 thru 9, and three plates. Then go play golf.

sum Any three of these ways
5 5 4+1 2+3 1
6 6 5+1 4+2 1
7 7 6+1 5+2 4+3 4
8 8 7+1 6+2 5+3 4
9 9 8+1 7+2 6+3 5+4 10
10 9+1 8+2 6+4 1
10 9+1 6+4 5+3+2 1
11 9+2 8+3 7+4 6+5 4
12 9+3 8+4 7+5 6+4+2 4
13 9+4 8+5 7+6 7+3+2+1 4
14 9+5 8+6 7+4+3 7+4+2+1 4
15 9+6 8+7 1+2+3+4+5 1

best wishes
--
Bernard V Liengme
www.stfx.ca/people/bliengme
remove caps from email

This is shameless I know, but I'm stuck with my daughter's homework
question. Here's the question -

"Nine eggs numbered 1 to 9. Put the nine eggs into three baskets. The
total
of the numbers on the eggs in each basket must be the same. How many
different ways are there to do it?"

As it's not stated to the contrary, I assume each basket can contain any
number of eggs, though each basket must contain at least one egg and
hence a
maximum of seven eggs.

No doubt can be solved with VBA, but here's the rub - this is for a
twelve
year! There's got to be a catch ?

Anyone interested in a virtual merit...

Regards,
Peter T