The Puzzle Thread

[Snowcrafta]

Re: The Puzzle Thread

12^2 (4+16/6x4) / 12-(4-2) x 0.5

[MinaciousGrace]

Re: The Puzzle Thread

y do they call it circular logic

becuz that's what it's called

[rushyrulz]

Re: The Puzzle Thread

Easy:

Flip this triangle upside down, but you may only touch 3 discs.

Medium:
What is the largest number you cannot make by adding multiples of 6, 9, and 20?

Medium-Hard:
What is the next number in the sequence?

1
11
21
1211
111221
312211

[leonid]

Re: The Puzzle Thread

Easy

   A
  O O
 O O O
B O O C

A O O B
 O O O
  O O
   C

Medium

43 cannot be made from 6, 9, 20

44 = 20 + 6x4
45 = 9x5
46 = 20x2 + 6
47 = 20 + 9x3
48 = 6x8
49 = 20x2 + 9

50 and higher can be made with 44~49 + 6xN

So the largest number that cannot be made is 43

Medium-Hard

1
11 One 1
21 Two 1's
1211 One 2 and One 1
111221 One 1, One 2, and Two 1's
312211 Three 1's, Two 2's, and One 1
13112221 One 3, One 1, Two 2's, and Two 1's

I already knew about this sequence so I didn't really solve it

[leonid]

Re: The Puzzle Thread

Here's one of my favorite math puzzles:

Me: Here are integers A and B, both greater than 1. Bob is given AxB and Sam is given A+B.
Me: Bob, do you know what A and B are?
Bob: I don't know.
Me: Bob doesn't know. What about you, Sam?
Sam: I don't know, either.
Bob: Ah! I know what they are.
Sam: I as well know what they are.

What are A and B?

EDIT: Let's just say A<=B to prevent confusion

[___________]

Re: The Puzzle Thread

A census taker approaches a house and asks the woman who answers the door "How many children do you have, and what are their ages?"

Woman: "I have three children, the product of their ages are 36, the sum of their ages are equal to the address of the house next door."

The census taker walks next door, comes back and says "I need more information."

The woman replies "I have to go, my oldest child is sleeping upstairs."

Census taker: "Thank you, I now have everything I need."

What are the ages of each of the three children?

[VisD]

Re: The Puzzle Thread

2,2,9

[igotrhythm]

Re: The Puzzle Thread

Here's one of my favorite math puzzles:

Me: Here are integers A and B, both greater than 1. Bob is given AxB and Sam is given A+B.
Me: Bob, do you know what A and B are?
Bob: I don't know.
Me: Bob doesn't know. What about you, Sam?
Sam: I don't know, either.
Bob: Ah! I know what they are.
Sam: I as well know what they are.

What are A and B?

EDIT: Let's just say A<=B to prevent confusion

If Bob has AB, then AB must be a number that has more than one way of being factored into two numbers each greater than 1. Thus, the smallest number Bob could have gotten is 12, which has factorization of 3*4 and 2*6. Thus, he can't give an answer. Since Bob can't answer, Sam can't answer either because his number likewise has more than one breakdown of A+B from the given integer...only this time, Sam's number can be no smaller than 6.

Bob now realizes that there is a second way of breaking down Sam's given number. The rest of my answer depends on whether Bob and Sam know each other's numbers.

[leonid]

Re: The Puzzle Thread

They don't know each other's numbers, otherwise their conversation is meaningless as they have the same information

[L.B.D.D]

Re: The Puzzle Thread

does it look like i know what a jpeg is

[___________]

Re: The Puzzle Thread

Here's one of my favorite math puzzles:

Me: Here are integers A and B, both greater than 1. Bob is given AxB and Sam is given A+B.
Me: Bob, do you know what A and B are?
Bob: I don't know.

As igotrhythm said, this means AB can be broken down in more than one (proper) way.

Me: Bob doesn't know. What about you, Sam?
Sam: I don't know, either.

Bob's combinations of possible A's and B's also both give numbers that can be broken down in more than one (proper) way.

Bob: Ah! I know what they are.
Sam: I as well know what they are.

What are A and B?

A+B can't be too high nor too low. A little bit of guess-and-checking gives A = 2 and B = 6. We see that this pair of numbers satisfies all requirements.

[igotrhythm]

Re: The Puzzle Thread

The problem with Underscoreman's solution is that those aren't the only numbers that satisfy the requirements. A=3 and B=4 would do it as well.

[___________]

Re: The Puzzle Thread

False. 2*5 = 10 can only be broken down in one way (other than 1*10)