Good girls and bad boys (8)

Logic Level 3

On an island, there is this strange pattern - boys always lie while girls always tell the truth. This time round, you encounter four children.

The oldest one says, "At least one of us is a boy."
The second one says, "At least two of us are boys."
The third one says, "At least three of us are boys."
The youngest one says, "All four of us are boys."

Convert the four children to a number based on their order of birth. Then submit your answer as the sum of the numbers of the boys only . For example, if you think only the youngest child is a boy, then your answer is 4. If you think only the middle two children are boys, then your answer is 2+3=5.

The answer is 7.

2 solutions

Noel Lo
Jan 27, 2016

This is seemingly similar to version #7 except for the fact that the word exactly has been replaced with at least. So this would not be so straightforward.

Now suppose out of four children, x of them are truthful. This means x are girls so the number of boys must be (4-x). If there are (4-x) boys, then the number of boys can be at least 1, 2,.... (4-x). This means (4-x) statements are true. So the value of (4-x) must correspond to that of x.

4-x=x

2x=4

x=2

So we have 2 boys and 2 girls. This means only the two older children are telling the truth. So the two older ones are girls while the two younger are boys (girl, girl, boy, boy).

The answer we are looking for is 3+4=7.

Saya Suka
Mar 17, 2021

If we tweak the statements a little bit, with exchanging at least into at most, boy(s) into girl(s) and the number n into 4-n, then we'd have : -

A : At most three of us are girls.
B : At most two of us are girls.
C : At most one of us are girls.
D : None us are girls.

Obviously, D is a boy since anyone saying that statement is also incriminating themselves by that shameless, seemingly paradoxical lie. By this, we know that AT LEAST one of the older siblings must be his sister, and because A's statement is the most open, positive and non-restrictive one among all others, then A must be D's oldest sister.

Can there be more girls? Yes, because by what A said it seems that it's possible until that new sister said something else that limit (NOT contradict) the number given by A earlier. So we accept the most non-restrictive true statement from all possible options, so the second sister is B who told that the maximum capacity for girls is 2, and thus we reached the new limit by the speaker herself. The siblings must have been comprised of Sister A, Sister B, Brother C and Brother D, for 2 total boys and a boy-sum of 3 + 4 = 7.

Good girls and bad boys (8)

The answer is 7.

2 solutions

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