# What is the maximum possible number of different pairs of chairs in which Frank and Ruby could sit?

zuhal on December 4, 2019

Can someone explain the question.

How does answer C is possible on first question? Can someone explain please.

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Ben on December 4, 2019

Hi Zuhal, thanks for the question!

This game has a major inference that we can use to our advantage. If there are 4 boys seated in 7 chairs, and no two boys can sit beside each other, then the boys must be seated in chairs 1, 3, 5, and 7.

The rule regarding Ivan is a convoluted way of saying that I sits 5th. So far we have _ _ _ _ I _ _

S sits east of I, giving us: _ _ _ _ I S _

F and R are together. We don't know who is west or east of the other. This block cannot fit in 7 (evidently). F is a boy and can therefore only sit in 1 or 3.

Since R is attached to F, we get these following scenarios.

F R _ T I S _ (we placed T in 4 because it is the only remaining slot for a girl) - H and J are interchangeable in 3 and 7

_ R F T I S _ (again, T in 4 because it is the only remaining slot for a girl) - H and J are interchangeable in 1 and 7

_ T F R I S _ (T is placed in 2 because it is the last remaining slot for a girl) - H and J are interchangeable again in 1 and 7

These are the three possible combinations that F and R can occupy and that is how we get answer choice C.

I hope this helps. Please let me know if you have any other questions.

Shitong on March 10 at 03:50AM

When it asks different pairs of chairs, does it mean that the combination is different?

Emil on March 12 at 08:43PM

That is indeed what that means! Since we know that f is immediately next to R, I think this is just asking us how many places our F R block could go. This is confusingly worded since f and r are theoretically interchangeable, but the boy girl rule means that there are no cases in which we could have swapped f and r and both scenarios would have been valid.