Question: Sum Sam and Product Pete are in class when their teacher gives Sam the Sum of two numbers and Pete the product of the same two numbers (these numbers are greater than or equal to 2). They must figure out the two numbers.
Sam: I don't know what the numbers are Pete.
Pete: I knew you didn't know the numbers... But neither do I.
Sam: In that case, I do know the numbers.
What are the numbers?
I confess I googled the answer. Man i got rusty with maths.
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Well I first thought it was 2,4 until I looked it up. Guess i'm still bad at math
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^___^
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tnx
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This comment was deleted 3 years ago.
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Too.. much.. thinking..
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Thanks!
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Thank you!
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Thanks :)
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Ugh... math. Product is when you multiply those numbers right? My first answer is 2 and 2 but it wouldn't make sense since Sam would know an easy thing like that!
Maybe 11 and 2? Sam gets 13 and Pete gets 22.Edit: Oh crap, so the sum guy is the one who knows and no the product guy... whoops, I suck at math! Lol
Edit2: I googled the answer, my head hurts hahaha
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Greats ! I like logic problems.
Sam doesn't know, so several possibilities. Pete doesn't know, so several possibilities too. But if after, Sam knows, only one possiblity is not obvious with the product. And it's seem to be some little numbers, otherwise there are too much possibilities.
I'm not sure if I'm clear, specially that my english is not perfect ... So, after 30 minutes to decrypt and scribble, I think that is 3&4 (sorry I don't know how hide text :S)
EDIT : and also Thanks for the giveaway of course ^^
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Thank You!
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Thank you!!!
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Thank You
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Meh, I liked the riddle more when it was about figuring out someone's birthday.
Thanks for the giveaway!
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thanks!
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thx
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The numbers are 3 and 4.
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So... the two numbers would be 2 and 2 since adding or multiplying them would both equal 4. That's my guess.
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They don't necessarily have the same answer. Actually, they definitely don't have the same answer (aka 4), otherwise they directly would know (since the numbers are greater or equal to 2, having 4 is pretty much a giveaway the two numbers are 2).
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There's nothing to say they numbers are NOT 2 because neither one is given the specific numbers, only the sum and product of the numbers. So they very well could be 2 and 2. So unless we know what the sum and product are, we can't pinpoint the numbers, as their own ability to figure out what the numbers are is irrelevant. The next step would be to tell each other what the sum and product are. Without this information I don't see how else to figure it out except to guess. However, 2 and 2 would undoubtedly work. Therefore, I'm sticking with it.
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If the numbers were "2", then Pete would know already his number (the product would be 4, and since numbers are greater or equal to 2, then the only possibility would be 2 by 2) and Sam would also know (since if the number were 2 and 2, the sum would be 4, and having a sum of 4 and knowing both numbers to be greater or equal than 2, the only possibility would be 2 and 2).
Since they both mentioned NOT knowing what numbers they have, that exclude 2 and 2, as well as a a few more (check my post later).
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But their intelligence isn't part of it. Those could very well be the numbers and they're too stupid to know it. They actually make no mention to each other of what their sum and product are so they can't do much to begin to guess. Of course they don't know what numbers each other has because they never even exchange the little, necessary information they DO have. And notice how at the end Sam DOES know, but there's no way to see if that's true or not either because you're taking his word for it. Their conversation carries no weight.
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Well, the conversation is pretty much the only hint you have, beyond the fact that their numbers are both greater or equal to 2.
Let's reverse it and prove the answer while respecting all the hints we have. Since we know the answer is 3 and 4:
Sam has received 7 as a sum.
Pete has received 12 for his sum.
Sam doesn't know the numbers (could be 2 and 5 or 3 and 4). He says so.
Pete doesn't know the numbers (could be 2 and 6 or 3 and 4). and knows Sam wouldn't know his numbers (since the only way he'd know is if he had 4 (knowing it would be 2 and 2) or 5 (2 and 3), both of which don't fit his 12).
Since Pete said he didn't know his answer, Sam can remove the 2 and 5 (product 10, which is only attained by those 2 numbers), so he now knows the right numbers are 3 and 4.
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But there's no reason to assume what their answers are outside of guesses. Neither one says what their sum or product is so you can't just assume the numbers for them blindly. Them knowing the two numbers is irrelevant entirely because they wouldn't even know what each other has for a sum and a product. This bit of information is crucial because, what if they had a sum and product of 4? There's nothing that disproves this being the case. So there are a lot of possibilities that open up due to us missing key information that realistically these two would know since they were told the sum and product. If they exchanged their information and it was part of the puzzle, you would be correct, but nothing says those are the sum and product, nor what the two numbers are, so we don't have enough information to solve this properly when they realistically would if they communicated.
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If they could tell each other their operation's result, then it becomes an algebra thing (a + b = y, a * b = z, knowing y and z figure out a and b). Now it's more of a logic question.
Let's see the case for the numbers of 2 and 2:
Sam receives the sum 4. Pete receives the product 4.
Sam would directly know the numbers are 2 and 2 (since that is the only possibility for a sum of 4 with numbers greater or equal to 2).
Pete would directly know the numbers are 2 and 2 (since that is the only possibilty for a product of 4 with numbers greater or equal to 2).
What disproves this case is the fact they would know the correct answer from the start, which the conversation shows they don't.
I'll repost what I did, if we go the route without guesses:
Let's start by removing some possibilites.
Since both numbers are greater or equal to 2, that removes the prime numbers (2,3,5,7,11,13,17,19,23,29...) as the product's result. For Pete not to know the number, his product wouldn't be from 2 prime numbers (4,6,9,10,14,15,21,22,25,26....) (or a number which is the product of the same prime (8 (2 x 4), 27 (3 x 9)).
For products under 30, that leaves the following products: 12,16,18,20,24,28
If he has a product of 12 (could be 3 x 4 or 2 x 6), 16 (could be 2 x 8, 4 x 4 ), 18 (could be 2 x 9 or 3 x 6), 20 (could be 2 x 10, 4 x 5), 24 (2 x 12, 3 x 8, 4 x 6), 28 (could be 2 x 14 or 4 x 7), 30 (could be 2 x 15, 3 x 10 or 5 x 6).....) than Pete wouldn't know, but with that Sam would know. Probably other answers further down the line.... Maybe I missed something.....
Possible numbers:
3 and 4 (s = 7)
2 and 6 (s = 8)
2 and 8 (s= 10)
4 and 4 (s = 8)
2 and 9 (s=11)
3 and 6 (s=9)
2 and 10 (s=12)
4 and 5 (s=9)
2 and 12 (s=14)
4 and 6 (s=10)
3 and 8 (s=11)
4 and 7 (s=11)
2 and 14 (s = 16)
2 and 15 (s=17)
3 and 10 (s=13)
5 and 6 (s=11)
From those, we removed the values with more than 1 of the same sum (since Sam now knows the answer).
That leaves 3 and 4. There is the possibility for greater sums than 11, but we can assume the upper sum come back (for example, if the product had 32, we could assume the numbers 4 and 8 would be also a possibility, rendering the 2 and 10 up).
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But again, you're assuming that they've discussed what their sum and product is, but they haven't. They only say if the know the numbers or not, which has nothing to do with the puzzle because one could understand it and the other might not. We're not given enough information from our perspective to figure it out to a certainty. Therefore, there is no absolute solution in this case. Follow me?
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I'm not assuming they told each other their answer, quite the contrary in fact. Only if they could deduce the numbers or not with the information they had, and whether or not the other could deduce it.
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Then even if they both had 4 and 2 and 2 were the numbers then it would work because they never discuss what numbers they have. So because they exchange no information except their claims on knowing the numbers or not, which still tells us nothing of what they do or do not know, we're still at the point of not knowing enough information to know the answer. We could only guess from a pool of possible answers with the current information. The only way to say it can't be 2 and 2 is to assume they discuss their sum and product, which they do not.
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It cannot be 2 and 2 because if it were, they could deduce it via their sum or product without exchanging information, while they say they can't deduce the numbers of either their sum or product.
For example, if Sam had received the sum of 5, even without speaking to Pete, he would know the numbers are 2 and 3. If he received the sum of 4, he would know the numbers are 2 and 2. If he had received a sum of 6 (or higher), he wouldn't be able to deduce the numbers (since there are a couple of possible answers, like 2 and 4 or 3 and 3, in the case of 6). Since Sam says he can't deduce his numbers, we can assume the sum he received is above 5. The only thing he'll say is he can't deduce his answer (from lack of information to narrow down his possibilities).
In the case of Pete, it's more complicated, since a product opens a lot of possibilities. First, the product he received cannot be a prime number (since either number is a minimum of 2, a prime number is not a possible product).
Second, since he couldn't deduce his numbers from his product, we can remove a few more answers. First, we can remove a product from two prime numbers, since he could deduce them. For example, if he received a product of 15, he would know the number are 3 and 5, since it is the only possibility.
We can also remove a prime multiplied by the same prime squared. For example, if he received 27, he would know it is 3 x 9, since that is also the only possibility, so he would be able to deduce his answer.
Since he can't, here are a few products that Pete wouldn't be able to deduce:
12,16,18,20,24,28,30....
With these numbers, Pete can't deduce the numbers (from lack of information to narrow down his possibilities), and will only say so. This, in turn, is an information that could help Sam narrow down his answer, but only one case.
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Oh, I see what you mean. That is, of course, assuming they know the math. However, how do you know it has to be 3 and 4?
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So, I said Pete couldn't deduce the following numbers:
12,16,18,20,24,28,30....
Let's see what numbers that would give us as possibilities:
Possible numbers (in parentheses, the sum of those numbers):
Product 12: 3 and 4 (s = 7) or 2 and 6 (s = 8)
Product 16: 2 and 8 (s= 10) or 4 and 4 (s = 8)
Product 18: 2 and 9 (s=11) or 3 and 6 (s=9)
Product 20:2 and 10 (s=12) or 4 and 5 (s=9)
Product 24: 2 and 12 (s=14) or 4 and 6 (s=10) or 3 and 8 (s=11)
Product 28: 4 and 7 (s=11) or 2 and 14 (s = 16)
Product 30: 2 and 15 (s=17) or 3 and 10 (s=13) or 5 and 6 (s=11)
Sam says he now knows. Which means from the above possibilities, there is one which only has one plausible answer. For this, we removed the values with more than 1 of the same sum. That removes the possibilities of numbers with a sum of 8,9,10,11 from the above, since if the sum of numbers were those, Sam still wouldn't know which number he had. For example, with the information from Pete (not knowing), and his sum (8), he would know the numbers are not 3 and 5 (otherwise Pete would have known), but doesn't know if it's 2 and 6 or 4 and 4.
That leaves a sum of 7. With the information that Pete doesn't know, that removes the 2 and 5, leaving only the 3 and 4.
There is the possibility for greater sums than 11, but we can assume the upper sum come back (for example, if the product had 32, we could assume the numbers 4 and 8 would be also a possibility, rendering the 2 and 10 up).
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Thanks!
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Thank!)
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Thank you! :)
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Thanks !
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