# Which one of the following runners must the coach select to run in the track meet?

Skyler-Simon on July 8, 2020

how were you able to deduct that T must be in from the first rule

how were you able to deduct that T must be in from the first rule - I do not understand how you made that jump

Replies

shunhe on July 10, 2020

Hi @Skyler-Simon,

Thanks for the question! So we know that there are five total runners, QRSTU. And we know that we have to pick 4/5 of those runners. So that means that 4 runners are going to be ‘in,’ and 1 runner is going to be ‘out.’

Well, let’s see if we can make T the runner that’s out. If we don’t pick T, then by default, we pick the other 4; we pick QRSU. But now look at rule 1! It tells us that if we pick Q, then we pick T (and T runs right after Q). And we just picked Q, which means we were supposed to pick T! But we didn’t, so we violated the first rule. So it’s impossible to leave T out; we have to pick T no matter what because of the first rule and the fact that we have to pick 4/5 runners.

Hope this helps! Feel free to ask any other questions that you might have.

hfatima1 on July 19, 2020

Hey shunhe,

Using the same logic as described above. the rule says if Q then QT box, so isn't the rule also telling us that Quinn is must? Or, am i wrong because Q is sufficient for Q and T and T is necessary? Does that make sense?

bingolawyer on July 31, 2020

Hi, I have the same question as @hfatima1. Thank you

bingolawyer on July 31, 2020

Never mind!!