He said “older”, with 3 people it should be “oldest”, so I guess that’s a hint that 2 had the same age.
This is a classic one. You flip the first switch and wait a while. You then flip the first one off and the second one on, and then entire the room. If the light bulb is off but hot, the first switch operates it. If the light bulb is on, it is the second switch. If it is off and cool then it is the third.
Start both hourglasses. When the 4 minute one runs out, then flip it over. When the 7 minute one finishes, there will be one minute left on the 4 minute glass. Start timing then. When the 4 minute finishes, you will have measured one minute. Two flips of the 4 minute gets you 8 more to yield 9 minutes.
You ask what the other guy would say, and then go through the opposite door.
If you talk to the honest one, he will honestly tell you which door the liar would call the safe passage, i.e. the bad door.
If you talk to the liar, he will lie and give you the opposite answer of the truthful guy, i.e. the bad door.
Thus, no matter who you are talking to you will get the “bad door” as the answer. That allows you to choose the good door by doing the opposite.
No need to assume, it’s a given, but nonetheless, the correct answer is none. Perhaps the OP meant to ask instead what is the minimum number of candies the merchant will have to sample to correctly label each box with 100% certainty? As phrased, he can correctly label them by guessing. Oh, semantics!
Mmm that would be an unsatisfying explanation. Unless the twins came out side by side one is still going to be older than the other. Besides, this isn’t the Bernstein Bears. No one refers to their kids as oldest, older, and youngest. The older one typically does refer to the oldest.
In generally accepted English usage, “older” is the older of two and “oldest” is the oldest of more than two. You wouldn’t use “older” to talk about any of three children.
I also grumble at that explanation. If there are 3 objects, mentioning that one is “the heavier one” in no way implies that the other two are the same weight; it’s just poor usage. And when it comes to kids from the same mother, one child is definitely older than the other even if they’re from the same delivery.
I also felt the answer to the first problem as stated was “none”.
“Mixed, mint, anise” and ‘anise, mixed, mint’ are both possibilities. To distinguish, he has to check the third box.
For the hourglass riddle, here’s a way to measure 9 minutes from the start: start both timers, when the 4 minute one is done, flip both over, 3 minutes are left on the 7 minutes timer. when those run out, 7 minutes has passed, and there is one minute left on the 4 and 0 on the 7. now flip the 7 and let the 4 run out its minute- now 8 minutes have passed overall, and one minute has passed through the 7- flip it over and when it runs out, 9 minutes total will have passed.
On the piano playing girls…
Clearly the key to the question is that the student knows the piano teacher’s house number … otherwise he would say “I don’t know your house number”. The fact that he says “I’m missing one piece of information” tells us that he does know the house number and that there are two possible sums of 36-factors that add up to it. The teacher’s answer about his oldest tells us that the differentiating factor between these two is that one has a single “oldest” and one doesn’t.
So 4,3,3 is excluded, not because 4-year-olds don’t play the piano, but because 4+3+3 is the only sum of factors that adds up to 10. On the other hand, both 9,2,2 and 6,6,1 add up to 13, so clearly those were the two the student was deciding between when he asked his final question.
It’s stated to us, in our role as the observers of the enigma. To be truly rigorous, we have to specify that the merchant has that information as well.
The trick with this one is that we don’t know the teacher’s house number, but we know the student knows it. We also know that knowing the sum and the product doesn’t give him a unique solution (since he says that’s not enough info), so we’re looking for two sets of factors which both sum to the same number: 9,2,2 and 6,6,1 both sum to 13. When he finds out that there’s an “oldest”, he knows it’s 9,2,2.
The mother’s age works out to 20 1/4 years, and the son’s age to -3/4 years (I’ll assume that people know basic algebra, so I won’t show the steps in figuring this out). The son’s negative age means he hasn’t been born yet. -3/4 years is nine months, which means the son has just been conceived. The father is smoking a cigarette.
Mine DOES play the piano
Perhaps I’m just persnickety but two things came to mind about this problem:
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With mint and anise candies he could probably just sniff them.
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Who’d want to buy a box of candies that someone had already sampled?
In a logic problem like this, the main thing you want to do is avoid tasting the mixed box. Let’s say there were 100 candies in the mixed box, 50/50 mint/anise. We would have to sample up to 51 of them to make sure it was the mixed box.
As the goal is tasting the least number of candies, tasting the “mixed” box is the only way to ensure that we aren’t tasting the mixed box.
Is this the credited answer? I hope not because it is a crap setup. Just like #2 with the “older”.
Nobody speaks of a just conceived child as being -3/4 years old, so the setup is bogus.
I agree with others that just because you have a set of twins, you wouldn’t call the senior sibling the “older”. She is one of three, even though two are (roughly) the same age.
If you had two Ford Escorts and one Jaguar, would you say that the Jaguar is the “more expensive” car? Of course not. It is the “most expensive”.
On the contrary, it’s simply thinking outside the box. I think it’s a well crafted puzzle since once you do the math it’s clear that it’s the only solution that lets you answer the question.
I disagree. It’s breaking all of the rules of convention. Nobody is negative number of years old. That is not used in any context.
Plus if you want to be technical about it, pregancies don’t last exactly nine months. It could have been shortly before or after the nine month period, and the father could have been doing whatever. He could have even been dead at that time. Maybe the father doesn’t smoke.
Also, the way these cute little riddles are worded, there are about 5 other interpretations that can be gathered (like with the above candy example) and those are simply dismissed as incorrect because it isn’t what the riddle’s author was thinking.
The candy solution is pretty straightforward and unamibuous (with the caveat that the merchant knows that all the labels are wrong). He can 100% positively identify all the boxes by tasting one candy.
The “9,2,2” solution doesn’t depend on the differnce between “older” and “oldest.” It’s only important that the clue indicate that the non-twin is older than the twins. I like the riddle better when it makes it clear that the additional information allowed the student to solve the riddle - then you know that he knew the teacher’s house address already, and the fact that one daughter was older than the other two is necessary to distinguish the correct answer from the other possible math solution (9,2,2 vs. 6,6,1).
The other one is a simple math problem. I know we don’t normally talk about negative ages, so it’s pretty contrived, but if you do the math and get -3/4, it’s not a trick question.
The third one
I guess we’ll agree to disagree. No, negative age isn’t commonly used, but once you do the math it becomes immediately apparent. If you did the math and then had to make some tortured leap of logic, I would agree. But the logic, once you arrive at the solution, is clear and simple. As to exactly what the father is doing isn’t important. It’s allowed a bit of leeway at that point in the process. 
I think that the candy solution is clear and simple as well. There’s no other interpretation that make sense based on the way it was presented. It’s extremely straightforward in my mind.