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In the Gadsden Diving Championships there is a panel of three judges. There are 12 scorecards with the numbers 1-12 on them, which are distributed so that each judge has four. After the diver has performed their routine, the judges each hold up a score card, and the diver's score is the sum of the three scorecards added together.

So, my question is:

What are all the different ways that the cards can be distributed among the judges, if all player scores from 6-29, except 10, were possible? Also, explain why ithere's no other way of distributing the scorecards. (other than swapping sets of 4 scorecards between judges)

Working Out:

I've already worked out some combinations, such as

View attachment 8172

Are there any others? Thanks!

So, my question is:

What are all the different ways that the cards can be distributed among the judges, if all player scores from 6-29, except 10, were possible? Also, explain why ithere's no other way of distributing the scorecards. (other than swapping sets of 4 scorecards between judges)

Working Out:

I've already worked out some combinations, such as

View attachment 8172

Are there any others? Thanks!