Kids' favorite colors

Logic Level 3

Mr. and Mrs. Lo have four children--Ann, Brenda (girls), Craig and Dean (boys). Each child has a distinct preference for their favorite color: blue, green, pink, or red (not necessarily in that order).

Here are some facts:

Ann is two positions away (in order of birth) from the person whose favorite color is red.
Of the two people whose respective favorite colors are red and pink, one is the oldest but the other isn't the youngest.
Brenda is a consecutive sibling with the person whose favorite color is blue.
Craig is younger than the person whose favorite color is green.

What is Dean's favorite color?

Pink Blue Green Red

1 solution

Noel Lo
Sep 14, 2016

Considering fact 2, we can rule out the red and pink as the favourite colour of the youngest child. Considering fact 4, we can also rule out green as the green lover must have at least one younger sibling. This means the youngest child likes blue. From fact 3, Brenda must be the third child.

1	2	3	4
?	?	Brenda	?
?	?	?	Blue

From fact 2, the green lover cannot be the oldest as the oldest likes either red or pink. This means the green lover is either second or third. From fact 4, this would mean that Craig is either the third or fourth child but since Brenda is the third child, Craig must then be the youngest.

1	2	3	4
?	?	Brenda	Craig
?	?	?	Blue

At the same time, consider fact 1. Ann is either the first or second child. If Ann is the second child, then the red lover would be the youngest but this contradicts with the fact that the youngest child likes blue. Hence Ann is the first child. Then the red lover would be the third child. Since the red lover isn't the oldest, then the pink lover is.

1	2	3	4
Ann	?	Brenda	Craig
Pink	?	Red	Blue

The only place Dean can go is the second place and the only possible favourite colour for him is $\boxed{green}$ .

1	2	3	4
Ann	Dean	Brenda	Craig
Pink	Green	Red	Blue

I think I solved this one a little different than the way you did. I solved it as follows anyway.

From 4 we know that the one who likes green is 2 positions older than Craig so in order for there to be any palce were we can place the one who likes green since there are 4 children he should be on either of the places first or second because otherwise there will be no place for Craig to be in the family and the system proposed would be inconsistent. We know from fact 2 that the oldest likes either pink or red therefore the one who likes green can't be the oldest remaining with the only possibility which enable us to further deduce that he is the second oldest and consequently that Craig is the youngest child from the four children anyway. We therefore have for a consistent problem _ g _ C the colors being noted with small letters the kids being named with the initials of their names and the blank spaces where we don't know either the color or the name of the child so to say noted as a " _ " sign. Now , we'll use fact 2 again from which we can deduce that because whatever is the colors which the oldest likes the other color isn't liked by the youngest either red or pink is on the 3nd therefore knowing that from all 4 colors neither of red , green or pink is liked by the yougnest which therefore should like blue. Therefore the solution looks like _ g _ Cb. Now ,we can use fact 3 from which we know that Brenda is consecutive sibling with the one who likes blue, i.e Craig. So we have until now the following thing so to say _ g B Cb. Now this seems complete enough to get the solution in more ways so to say. We'll just choose to use fact 1 which says that Ann is at a distance of 2 from the red lover from which we conclude that she must be the first child because he can't be a green liker since that would mean she is at a distance of 1 from whoever is the red lover and from the fact that Ann is oldest that Brenda likes red and Ann pink. Therefore so to say the problem gives the situation Ap g Br Cb and therefore Dean likes green.

A A - 4 years, 9 months ago

This is a good solution but I don't think it was originally said that Craig is two positions younger than the one who likes green anyway. If I remembered correctly, it originally just said that Craig is younger than the person who likes green but I think someone edited this part anyway. So I think you should correct this part in your solution anyway. The solution still works even with the original version anyway.

Noel Lo - 4 years, 9 months ago

Maybe you can argue it like this based on the originally version anyway:

Like you said, of all four colors neither of red, green or pink is liked by the youngest so the youngest likes blue which still holds anyway. Then Brenda would be 3rd from fact 3 anyway. Like you said also, the one who likes green can't be the oldest from fact 2 that the oldest likes pink or red anyway. Then whichever position the green lover is whether 2nd or 3rd Craig is definitely the youngest since Brenda is already 3rd anyway.

The rest follows accordingly.

Noel Lo - 4 years, 9 months ago

Yep , that is a good solution too and it's cute than you were attentive at some details and you so to say even used those anyway.

I have no idea why your problem was edited , in the original version it was a little harder and change done is truly irrelevant anyway.

A A - 4 years, 9 months ago

@A A – Yes I agree I didn't actually realise there was a change until I read your solution anyway. I thought the problem (in particular the fourth clue) was still the same even after being reshared anyway.

Noel Lo - 4 years, 8 months ago

Oh , you're solution is cute too anyway.

It's nice though to keep a flexible thinking and try finding alternatives anyway.

A A - 4 years, 8 months ago

Btw this is another nice problem and it seemed to me to be more synthetic in the character it alluded and displayed anyway.

It's interesting to get an understanding of the process of how you complete missing information in a systematic manner using simple inferences and to analyze such an derivation at broad along with the various way by which they can be made and expressed in general to arrive at a "proof" as you get a sense of deterministic understanding anyway.

A A - 4 years, 9 months ago

Kids' favorite colors

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