Jealousy makes things difficult

4 swimming competitors, ranked by the judges 1st - 4th, are lining up in a straight row for a photo. However, no swimmer wants to stand next to the person who ranked just above them. How many ways (if at all) can the swimmers be arranged?


The answer is 2.

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6 solutions

If 3 or 2 is on the inside , they would have to be next to either the one they finished just behind, or the one they finished just ahead of.

Example: if 3 is the second number listed, it won't want 2 in either the first or third spot. Which leaves 1 and 4 in those spots. However, 4 can't be in one of the spots adjacent to 3. The same logic, with the numbers reversed, applies to 2. So 2 and 3 have to be on the outside.

From there it is simply a matter of slotting 1 and 4 in the middle, next to their appropriate outside counterparts, (1 next to 3,as it can't be next to 2) and noting that the sequence can also be reversed with the same results.

2413, 3142

Correct! Others are wrong

Daniyal Ahmed - 5 years, 8 months ago
Fathan Ihsan
Sep 30, 2015

3142

2413

3412 is wrong... That puts 2 and 1 next to each other violating the rule...

Thomas Vallier - 5 years, 8 months ago

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edited, thanks

Fathan Ihsan - 5 years, 7 months ago
Suman Jain
Oct 13, 2015

As we know no two simultaneous rankers can't stand together so 4-3 2-3 Never can stand together,so 3 will only can come on corners and with 1 only and 1 can be with 4 on other side that's why solutions are 3142 or 2413

Jamie Forsythe
Oct 12, 2015

Since 2nd and 3rd both have a place on either side of them, this means there is only one place of the 4 that isn't next to each one (4th and 1st respectively). Therefore 2nd and 3rd can only be next to one place each, meaning they must be on the ends of the line. This means the possible combinations are 2143 or 2413, and the reverse of each of these. However, for 2143 2nd and 1st are next to each other, as are 4th and 3rd. Therefore the only possible combinations are 2413 and its reverse, 3142.

Prinshu Kumar
Oct 10, 2015

Only two possible ways. 2413 and 3142. This is because 2 and 3 can not be in the middle.

Sama El-Saadany
Sep 30, 2015

3124-4213-2413-3412

In both of your first two sequences, 1 and 2 are next to each other.

Josh Mcdevitt-Spall - 5 years, 8 months ago

3124 and 4213 are incorrect; 1 and 2 are next to each other.

Digital Gaming 227 - 11 months, 3 weeks ago

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