Double Quadruple Runners

Logic Level 2

In a marathon, there are 8 runners: 2 of them are wearing yellow shirt, 2 of them are wearing red shirt, 2 of them are wearing blue shirt, 2 of them are wearing green shirt.

At the finish line, their configuration is as follows:
- 1 runner between the red pairs,
- 2 runners between the blue pairs,
- 3 runners between the green pairs,
- 4 runners between the yellow pairs.

If we know that the last runner wore a yellow shirt, can you tell what colors all the runners are wearing (from fastest to slowest)?

Details and Assumptions :
- Denote $1,2,3,4$ as the runners wearing red, blue, green, yellow shirt respectively.
- If you think the arrangement (from fastest to slowest) is: Yellow, Yellow, Blue, Red, Blue, Green, Green, Red, then submit your answer as 44212331.

Too easy? Try the harder one .

Image Credit: Wikimedia Peter van der Sluijs .

The answer is 23421314.

2 solutions

Livy Smith
Jun 9, 2015

23421314

Blue, Green, Yellow, Blue, Red, Green, Red, Yellow.

We know that Yellow comes last and that there must be 4 runners between two yellow shirted people. We know there are 8 runners in total.

We end up with; x x Y x x x xY

We know that green must have exactly 3 runners between it so we end up with the options of;

G x Y x G x x Y or x G Y x x G x Y

Blue has 2 people between them and therefore can be inserted into the equations above.

G x Y B G x B Y or B G Y B x G x Y or x G Y B x G B Y

Red runners finally have only one runner between them. Therefore the only option left that works is the second option above.

B G Y B x G x Y = B G Y B R G R Y

Yes , right. Also observe that it is not necessary to know where the Y shirted fellows are.

A A - 5 years, 1 month ago

Abhay Tiwari
Jul 13, 2015

- - Y - - - Y, this is all we know after the end of the problem.

1) there is only 1 player between red that means red will be in between the two yellow T-shirt runners with the configuration as either - -Y R - R - Y or - -Y - R - R Y.

2)Now we have to decide which one is correct, the first configuration of the two above is wrong as if BLUE runner is placed at the first, then the second BLUE runner won't be able to fit in the configuration as his place is already taken by RED runner, as there are two runners between the blue runners.

3) Even if BLUE Runner is placed in the second position like this - B Y R B R - Y , this configuration won't get satisfied for the GREEN TSHIRT runners.

4) So now we move on with this configuration - - Y - R - R Y. Now if I place blue in the second position.The first RED runner will clash with position of second BLUE runner.

5) So the final position for BLUE runner is the first position for the BLUE runners and the configuration builds up like this B - Y B R - R Y. Now fill the GREEN runners and final configuration builds up as B G Y B R G R Y....

Double Quadruple Runners

Too easy? Try the harder one .

Image Credit: Wikimedia Peter van der Sluijs .

The answer is 23421314.

2 solutions

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