Thread: Math Question

*Edit*

Smoot is correct regarding your solution Cajun. I had a response typed out but it sucked :grin:

I am begining to wonder if it is even possible.

"Del Rio" wrote:

Ok I know someone on this site must be a math genious. So here goes. I am in charge of making a work list that will run for six months.

There are 12 guys, who will be working in groups of 2. And they will need to be in a different group every month (not grouped with the same people twice.)

That is fine and dandy, but the hospital has 6 floors, so not only do I need every group to be different each month I need each person to get the opportunity to work on each floor.

------------------------------------------------------------

I was thinking I would let each letter of the alphabet equal a person so you have

A B C D E F G H I J K L------------REPRESENTS EACH PERSON 12 TOTAL.

So if you draw a grid out 6months down the side- the floors over the top. and you start grouping the letters together.....AB, CD......so on it equals a huge pain in the azz. I have gotten 5 months done and 5 floors where no one is grouped together twice, and no one is on the same floor. But it is looking like there is only one possible solution to the problem.

So does anyone know an equation, a web site for an equation, or anything. $50.00 reward for the correct answer or a source that can help me get the right answer.

(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)
(A)(B)(C)(D)(E)(F)(G)(H)(I) (J) (K) (L)

***Jn Fb Mr Ap My Jn
(1) AG BI CJ DK EL FH
(2) AI BG CL DJ EH FK
(3) AK BL CG DH EJ FI
(4) AL BK CH DG EI FJ
(5) AJ BH CI DL EG FK
(6) AH BJ CK DI EL FG

Let me know if this is correct. I want my 50 bucks if it is ... J/K.

***Jn Fb Mr Ap My Jn
(1) AG BI CJ DK EK FH
(2) AI BG CL DJ EH FL
(3) AK BL CG DH EJ FI
(4) AL BK CH DG EI FJ
(5) AJ BH CI DL EG FK
(6) AH BJ CK DI EL FG

Jan has guy (A) working on every floor.
Feb has guy (B) working on every floor.
And so on.

Here is mine:
***Jn Fb Mr Ap My Jn
(1) AB CD EL GH FI JK
(2) CE FK HJ BI DG AL
(3) DF AE GK CJ BL
(4) GJ BH AI FL CK DE
(5) HI GL BD EK AJ
(6) KL IJ CF AD EH BG

You can go down the list of Jan and no letter is repeated, you can go across level 1 and no letter is repeated. It has to be that way all the way across all the way up and down.

I got this:


AB DE FH CL JK GI
CI AF EL HJ DG BK
DJ CB AK EG HI FL
GL JK BD AI CF EH
HK LI CG BF AE DJ
EF GH IJ DK BL AC

The only thing wrong I can see is DJ at (1,3) and (6,5)

Close but no cigar. :grin:

I'm pretty sure this is right:


AB CD EF GH IJ KL
EK AG CI BJ FL DH
CF BE AD IL HK GJ
DL FJ BH AK CG EI
GI HL JK DF AE BC
HJ IK GL CE BD AF

I say kill 6 people and then let one person work each floor for two months.
Sell the dead peoples organs and take a vacation.

But that is just me, I cut to the chase on stuff like this.

That is why I am President and CEO of my dogs fortune 500 company.
He says I am doing a great job, right Sam?

"canadian_vikes_fan" wrote:

I'm pretty sure this is right:


AB CD EF GH IJ KL
EK AG CI BJ FL DH
CF BE AD IL HK GJ
DL FJ BH AK CG EI
GI HL JK DF AE BC
HJ IK GL CE BD AF

Did you use a prgram to get it or just by grunt work?

Good work though.

"cajunvike" wrote:

Does this look right?

Months across, floors vertically.

...1..2..3..4..5..6
6 FG EH DI CJ BK AL
5 GH FI EJ DK CL AB
4 HI GJ FK EL AD BC
3 IJ HK GL AF BE CD
2 JK IL AH BG CF DE
1 KL AJ BI CH DG EF

What about THIS WAY?

...1..2..3..4..5..6
6 FG GH HI IJ JK KL
5 EH FI GJ HK IL AJ
4 DI EJ FK GL AH BI
3 CJ DK EL AF BG CH
2 BK CL AD BE CF DG
1 AL AB BC CD DE EF

No I just wrote it out on Excel and kept changing things when they were wrong. Only took me ~20 mins. I hope its right!

"cajunvike" wrote:

"cajunvike" wrote:

Does this look right?

Months across, floors vertically.

...1..2..3..4..5..6
6 FG EH DI CJ BK AL
5 GH FI EJ DK CL AB
4 HI GJ FK EL AD BC
3 IJ HK GL AF BE CD
2 JK IL AH BG CF DE
1 KL AJ BI CH DG EF

What about THIS WAY?

...1..2..3..4..5..6
6 FG GH HI IJ JK KL
5 EH FI GJ HK IL AJ
4 DI EJ FK GL AH BI
3 CJ DK EL AF BG CH
2 BK CL AD BE CF DG
1 AL AB BC CD DE EF

On the bottom row, A is working twice at once, or is on the same floor twice.