Can somebody explain why 7 is the result of the given test?

What is wrong with the following list of tuples:

1. 1 1 1
2. 1 1 2
3. 1 1 3
4. 1 2 1
5. 1 3 1
6. 2 1 1
7. 3 3 3

In this list of tuples, there is no tuple where all 3 elements have the same salary as before

Edited by author 18.04.2011 09:13

I think you're missing a few, for example:
2 2 2
1 3 2
etc.

The robot can't pay with rank1<rank2<rank3 & payment1>payment2>payment3 but he can do it if
rank1<rank2<rank3 & payment1<payment2>payment3.

Basically, for the 7 3 example you can do all permutations with repetition except for
3 2 1
so its 2 to the power of 3 minus 1.

I can see why 3 2 1 is not allowed (constraint rank1<rank2<rank3 & payment1>payment2>payment3) and that is fine.

But why 2^3? You have 3 options for salary for each of 3 robots, I would say it is 3^3 - 1?

Yes, the count of allowed configurations of salaries is 26. So the accountant-robot will rust in 27th month, i.e. in 7th month of the year. That's why the answer is 7.

thanks!

Pardon, it was a typo, I meant 3^3-1. :)