25 replies to this topic

[belwood]

Can someone explain to me why it is not 3 and 4?

Even without following the "rules", a sum of 7 would have given B the answer immediately upon hearing that A doesn't know the sum. because the product of 7's alternative pair (2,5) would have given the answer to A immediately.

[mistral]

I disagree with answer 2 and 9. Because:
first person know the product is 18. He don't know the answer now. He just could guess the set of the answer:
1x18 imposible, coz 1 not allowed
2x9 could be the answer
3x6 could be the answer
By know the sum is less than 14, he still don't know the answer coz
2+9 < 14
3+6 < 14
So he don't know the answer and couldn't say wether he know the answer

[rookie1ja]

I disagree with answer 2 and 9. Because:
first person know the product is 18. He don't know the answer now. He just could guess the set of the answer:
1x18 imposible, coz 1 not allowed
2x9 could be the answer
3x6 could be the answer
By know the sum is less than 14, he still don't know the answer coz
2+9 < 14
3+6 < 14
So he don't know the answer and couldn't say wether he know the answer

as mentioned in the solution ...
3 6 ... NO - it is impossible to create any pair of numbers from the given sum, where there would be at least one sum (created from their product) bigger than 14

if 3 and 6 then they would think the following ...
A teacher says: I'm thinking of two natural numbers bigger than 1. Try to guess what they are.
The first student knows their product (18) and the other one knows their sum (9).
First: I do not know the sum.
Second: I knew that. (pairs of numbers that have sum of 9 can have various products) The sum is less than 14. (here is the problem, I thought that there would be some other combination for which sum would be bigger than 14 and thus I would help you by eliminating that combination ... but for sum of 9 there is no such combination ... whereas for sum 11 there is - 7 and 4 - which would make the product of 28 - that could be 14 and 2 as well - so 16 is bigger than 14 ... the same for 8 and 3, 5 and 6)
First: I knew that. (there is no way to have sum of 2 numbers 14 or more, when their product is 18 ... but you must have thought that I do not know it - and that's the problem - you did not know that) However, now I know the numbers.
Second: And so do I.
What were the numbers?

[nobrains]

can sum1 tell y not 4,6.its product is 24 and v can even have 8,3 which have the same product and their sum is less than 14

[DarkSpin21]

Can someone explain to me why it is not 3 and 4?

he ment to put 2+5, this problem has made me pull my hair out for 2 days and i was convinced it was 2 and 6, but anyway, 1sponer or watever his name is explains the prosses the best

[puzzlmaster]

can sum1 tell y not 4,6.its product is 24 and v can even have 8,3 which have the same product and their sum is less than 14

Here's why it can't be 4 & 6. Follow the process:

First student doesn't know the sum: this is fine, he knows the product is 24 but the sum could be 10 (4+6), 11 (3+8) or 14 (2+12). It fails right here.

He also knows, per the 3rd line, that the sum is less than 14, so it can't be 2 & 12. However, if the product, which he knows, is 24, there is a possibility that the numbers are 2 & 12. Since there is this possibility he cannot possibly know that the sum is LESS (not equal) to 14. It is quite possible that the sum would be equal to 14, so this is a contradiction.

Edited by puzzlmaster, 23 April 2008 - 09:34 PM.

[Vishmi]

That was pretty hard since we have to think about all possible combinations.
But I don't understand why the solution should be 9 and 2.

Edited by Vishmi, 24 April 2008 - 07:56 AM.

[Lemeshianos]

Can someone explain to me why it is not 3 and 4?

It the numbers were 3 and 4 that means that one kid knows that the sum is 7.
The teacher said that the numbers were larger than 1. So the combinations that give you 7 and the nums are larger than 1 are:
2:5
3:4

The sum kid(kid that knows the sum) is aware that the product kid knows the product.
So if the other kid knew that the product was 10 then they wouldn't have the discussion because only 2 numbers give you a product of 10 and those are 2 and 5.
Since the product kid did not speak saying he knows the numbers, the sum kid is safe to assume that the numbers are NOT 2 and 5.
That leaves only one combination for a sum of 7 and that is the combination 3:4. The sum kid now knows this and would have spoken about what the numbers were.

Since none of the kids spoke about their numbers and had that discussion above, this means that the numbers were not 2:5 or 3:4

[Lemeshianos]

I disagree with answer 2 and 9. Because:
first person know the product is 18. He don't know the answer now. He just could guess the set of the answer:
1x18 imposible, coz 1 not allowed
2x9 could be the answer
3x6 could be the answer
By know the sum is less than 14, he still don't know the answer coz
2+9 < 14
3+6 < 14
So he don't know the answer and couldn't say wether he know the answer

Ok assume the numbers were 3 and 6.
State 1:
Sum kid knows the sum is 9. Possible combinations:
2:7 Product 14
3:6 product 18
4:5 product 20

State 2:
The 2:7 gives a product of 14. A product of 14 can only derive from 2 and 7. Product kid would need no help to figure out the numbers.
4:5 gives a product of 20 which has the combinations of State 3
3:6 which has a product of 18 and the combinations of State 4




State 3:
2+10=12 In this case the product boy assumes that the sumn boy knows the sum is 12. What could be going in the sum boys mind right now?
2+10=12 Product 20 Could be the answer
3+9=12 Nope product is 27 giving away the answer
4+8=12 Product 36 Could be the answer
5+7=12 Nope product is 35 giving away the answer
6+6=12 Product 36 Could be the answer

State 4:
3+6 = 9 Could be the answer
2+9 = 11 Could be the answer
Both have a sum less than 14

This gets too confusing to continue, but all you need to understand is that none of the boys can eliminate enough combinations to have only one combination left to speak the answer.
So the boys have to talk to each other to get some more info.
The sum boys says the sum is less than 14. After this statement, both boys know the numbers. At this point the product boy knows the numbers because he states so. The sum boy eliminates the combination he had that would have left the product boy in doubt, thus he figures out the numbes too.
BUT in the above example, the product boy doesn't figure out the numbers. Check state 3 and state 4. Both of them have combination that sum up to less that 14. So the product boy cant eliminate any combination. The sum at this situation doesn't help him. But in our example, the product boy had figured out the numbers after he know the sum was less than 14. So 3 and 6 are not the combination since the leave the boys still struggling to figure out the solution.

[arun]

You don't have to take all combinations to work this one out. It is based on the following:

If a number is the product of two primes, then you know their sum.

Clues:
A: I don't know the sum. So the number is not the product of two primes. One of the numbers must be 4, 6, 8, 9 or 10.

B: I knew that. This is the biggest clue! If the sum can also be a sum of two primes, then B would not be absolutely sure that A does not know the numbers eg if B's sum was 6, then it could be that A's product is 9=3x3, from which A could immediately deduce the two numbers. So the fact that B knew that A did not know the sum limits the sum to be 11. Every other number under 14 is the sum of two primes: 4=2+2, 5=2+3, 6=3+3, 7=3+4, 8=3+5, 9=2+7, 10=3+7, 12=5+7, 13=2+11.

So the possibilities are 2 9, 3 8, 4 7, or 5 6.

B: The sum is less than 14
A: I knew that. This implies that the product cannot be factored out into two numbers whose sum is larger or equal to 14. Now the largest sum that the factors can add to is when we take a large and a small factor. This eliminates 3x8=24=2x12, which allows 2+12=14;v or 4x7=28=2x14 with 2+14>14; or 5x6=30=2x15, 2+15>14; leaving only 2x9=18=3x6. So the numbers are 2 and 9.

This explanation is pretty neat and simple, thanks