Best...Puzzle...Ever....

[Sagiro]

Pielorinho, you're on the right track! I'm impressed to get such a quick and good reply. Honestly, it took me much longer to get as far as you got.

Unfortunately 2 and 9 is not the answer.

As you showed, if the sum is 11, A can be certain that B cannot find out the numbers. (It isn't the only number with this property. 17, for example, is another one.)

Now, if A tells B that he knows that B cannot find out the numbers, B knows, that 9 and 2 must be the answer, since he got 18, and that can only be factored as 2*9 or 3*6. 3 and 6 is impossible, because 3+6=9, and that can also be the sum of the primes 2 and 7 (if both numbers are prime, B would immediately know them from the product). So B knows the numbers.

But ...



It can't be 30, since 30 can also be factored 15*2 (as I said before, 17 is another number that allows A's statement). But 18, 24 and 28 are all possible factors, so A cannot know the numbers at this point.

So, 2 and 9 is not the correct solution.

As far as I can tell, this line of reasoning narrows the possible products down to ten possibilities:

18 (2, 9)
24 (3, 8)
28 (4, 7)
50 (2, 25)
52 (4, 13)
54 (2, 27)
76 (4, 19)
92 (4, 23)
96 (3, 32)
98 (2, 49)

...but I'll be darned if I can figure out how B is able to narrow it down further without additional information.

That last step's a doozie!

-Sagiro

 

[RithTheAwakener]

As far as I can tell, this line of reasoning narrows the possible products down to ten possibilities:

18 (2, 9)
24 (3, 8)
28 (4, 7)
50 (2, 25)
52 (4, 13)
54 (2, 27)
76 (4, 19)
92 (4, 23)
96 (3, 32)
98 (2, 49)

There is a fault with this, the riddle says

I am thinking of two numbers, both greater than 1 and smaller than 100. I will tell A the sum of those numbers (X+Y) and B the product (X*Y)

It say both numbers can be anywhere from 1-100. Which means it could be, for example, 99 and 87. So it would have many more possibilities for X*Y than ending at 98... unless im missing something, which is very possible, cause im an idiot.

 

[RithTheAwakener]

I am thinking of two numbers, both greater than 1 and smaller than 100. I will tell A the sum of those numbers (X+Y) and B the product (X*Y). If anyone of you finds out the numbers, he is free. But don't give each other any hints!"

After the villain has told A the sum and B the product, both are silent. Some moments of careful thinking later, B confesses: "Sorry, I have no idea, what the numbers were." A says: "Yes, I already knew that you couldn't find them out." - "Did you", B says, "In this case, I know them now." - A replies: "Okay, now I know them, too."

And indeed, after this conversation (which didn't seem to contain any hints - or so the villain thought), both knew the right numbers.

How did they do that, and what were the numbers?

Well. Its very late right now so I cant do it in my head, but i think it has to do with the number of letters and words in each of the first two sentances...

 

[Wippit Guud]

Here's one, and it isn't a math question!


A man lies in a bed, murdered. On the nightstand next to him is a pair of scissors. The scissors are the murder weapon. But there is no cuts on the body, and no blood. How did he die?

 

[Richards]

Spoiler

It's a hospital bed and the scissors were used to cut the man's IV bag/dialysis machine cord/direct oxygen feed tube/other life-sustaining equipment?

Johnathan

 

[Wippit Guud]

It's a hospital bed and the scissors were used to cut the man's IV bag/dialysis machine cord/direct oxygen feed tube/other life-sustaining equipment?

The man was 100% healthy when he went to bed. No hospital stuff or anything.

 

[kirinke]

Spoiler

Can you set the basin of fire below the basin of water to boil it, and take the empty one and turn it upside down to fill it with steam?

that would work. or simply take the water and pour it on the elemental fire (which can never be put out.) the steam would fill the room, which in turn would fill the bowl.

 

[der_kluge]

Spoiler

The scissors are a red herring. He had a heart-attack in his sleep and died.

 

[Richards]

Okay then...the scissors were used to cut the rope holding the 16-ton weight supported over the bed?

Or maybe they were the Norns’ scissors, and they were used to snip the man’s life thread?

Seriously though, could they have been used as a bludgeoning weapon? Or pressed against his carotid artery (is that what’s called?) until he passed out, then smothered with a pillow? (Hmm, I suppose that would actually make the pillow the murder weapon, and the scissors just an “accessory.”)

I have the feeling I’m going to feel pretty stupid when somebody comes along and points out the (no doubt) obvious answer.

Johnathan

 

[Richards]

die_kulge: The setup specifies that the guy was murdered, and that the scissors were the murder weapon.

Johnathan