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Happy New Year! The following question is abstracted from Singapore Mathematical Olympiad 2015 Junior Round 1.

Question 2: Adrian, Billy, Christopher, David and Eric are the five starters of a school’s basketball team. Two among the five shoot with their left hand while the rest shoot with their right hand. Among the five, only two are more than 1.8 metres in height. Adrian and Billy shoot with the same hand, but Christopher and David shoot with different hands. Billy and Christopher are respectively the shortest and tallest member of the team, while Adrian and David have the same height. Who is more than 1.8 metres tall and shoots with his left hand?

(A)None (B) Only Christopher (C) Only Eric (D) Christopher and Eric (E) Not enough information to ascertain

Now to spare you some time, this is the confirmed ones:

Left Handed: Eric
Right Handed: Adrian and Billy
Above 1.8m: Christopher and Eric
Below 1.8m: Adrian, Billy and David

Now left to decide of Christopher or David is left handed. Because no matter Christopher being left handed and right handed, it still follows the statement. Is it simply have not enough information to determine if Christopher and David is left handed?

Théophile
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ministic2001
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  • So the answer is E, isn't it? – fleablood Dec 31 '15 at 16:36
  • There are $4$ possible combinations. Eric qualifies in all of them, while Christopher qualifies in one of them (where both him and Eric are more than 1.8 metres tall and shoot with their left hand). Hence the answer is Eric for sure, and possibly also Christopher. – barak manos Dec 31 '15 at 17:12

1 Answers1

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You propose that there are at least two valid different scenarios that satisfy the conditions and therefore there is not enough information to solve. If that is the case, then yes that should be the correct answer. Let us check that both scenarios are valid

$\begin{array}{r|c|c|} &\text{Right}&\text{Left}\\ \hline \text{Taller than} 1.8m&&CE\\ \hline \text{Shorter than} 1.8m&ABD&\\ \hline \end{array}$

$\begin{array}{r|c|c|} &\text{Right}&\text{Left}\\ \hline \text{Taller than} 1.8m&C&E\\ \hline \text{Shorter than} 1.8m&AB&D\\ \hline \end{array}$

  • Two are lefthanded and three are righthanded: $\checkmark$
  • Two are taller than $1.8m$ and three are shorter than $1.8m$: $\checkmark$
  • $A$ and $B$ shoot with same hand: $\checkmark$
  • $C$ and $D$ shoot with different hands: $\checkmark$
  • $B$ and $C$ are respectively shortest and tallest members of team: $\checkmark$
  • $A$ and $D$ are same height: $\checkmark$

Indeed, both scenarios satisfy all of the given statements. Now let us look at the question:

Who is more than 1.8 meters tall and shoots with his left hand?

As we showed, it could either be only Eric or it could be Christopher and Eric. Since both are possible with the given information, the answer to give is (E) Not enough information to ascertain.

Given an additional piece of information, such as "There is only one tall left-handed player" then we could pinpoint it further.

JMoravitz
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  • Ah thank you. Usually, for mathematics contests, the answer wouldn't be "not enough information" which is why I was worrying so much when I couldn't figure out the remaining. – ministic2001 Dec 31 '15 at 16:44