Excel Challenge

  • Thread starter Thread starter JP SIngh
  • Start date Start date
J

JP SIngh

Guys

I have been given a very difficult task and I need help.
Please!!!!!!!!!!!!!!!!!

The issue has more to do with maths than excel.

What we have is 10 Athletes who will compete in 9 different competitions.
Each athlete with complete against every other athlete only once.

So the total number of match will be 45.

A v E B v E C v E D v E
A v F B v F C v F D v F E v F
A v G B v G C v G D v G E v G F v G
A v H B v H C v H D v H E v H F v H G v H
A v I B v I C v I D v I E v I F v I G v I H v I
A v J B v J C v J D v J E v J F v J G v J H v J I v J


We will film these matchs and need to produce 5 shows. This is where the
problem arises.

Every show must show all the nine completions and must not show each athlete
more than twice. I will need to come with a list of matches that can be part
of each show so that the above two conditions are satisfied.

Can this be done or it is too challenging?
 
Yours is a math question, rather than an Excel question.

For one solution, index a 10x10 rectangular array by A, B, ..., J going
down the rows and A, B, ..., J going across the columns. The lower left
triangle (below the diagonal) of this array then corresponds to all the
45 pairngs. Fill in that lower triangle as follows:

1
2 1
3 2 1
4 3 2 1
5 4 3 2 1
5 5 4 3 2 1
4 5 5 4 3 2 1
3 4 5 5 4 3 2 1
2 3 4 5 5 4 3 2 1

In case this is a homework problem, I will leave it to you to explain
why you can do it this way, or whether there are other essentally
different solutions.

Jerry
Excel MVP
 
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