Linked Questions

26 votes
3 answers

A game of multiplication and addition

Carol is playing a game with Alice and Bob. She secretly chooses two integers between 1 and 10 and gives the sum to Alice and the product to Bob. After some time, the following discussion occurs: ...
Untitpoi's user avatar
  • 2,690
10 votes
8 answers

When is Cheryl's Birthday? [duplicate]

I saw this question on Facebook: Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates. May 15 16 19 June 17 18 ...
Fodder's user avatar
  • 331
22 votes
3 answers

Sum of secret numbers is 101

Alice, Bob, and Charlie were given three numbers, respectively. They were said that all the three numbers were positive integers and the sum was 101. Alice: I know we have different numbers. Bob: ...
P.-S. Park's user avatar
  • 4,169
12 votes
6 answers

Find two numbers based on either their product or their sum?

A friend of mine told me the following puzzle and I could not solve it. Sam chooses a positive integer $x$, and Peter chooses another number $y$. They do this secretly, so that Peter does not know Sam'...
user11489's user avatar
  • 137
13 votes
3 answers

Who will find the number on their own hat first?

Both $A$ and $B$ have numbered hats on their heads. $A$ and $B$ both cannot see his/her own hat, but they can see other one's hat. $A$ sees number on $B$'s hat as $5$ and $B$ sees $A$'s number as $4$. ...
Tharindu Sathischandra's user avatar
10 votes
3 answers

Sum, Product and Difference

I had three mathematician friends at school, and we were hanging out. Out of the blue a question came to my mind, and I decided to ask it to them: "Guys, I have a question for you. Which is actually ...
Oray's user avatar
  • 30.2k
9 votes
3 answers

The heritage of a numismatic

The old rich Jeremiah has two sons, Timothy and Joseph. One day, Jeremiah decides to discuss about his heritage with his sons... JEREMIAH: Dear sons, I'm very old and exhausted, so I want to bequeath ...
leoll2's user avatar
  • 12.6k
7 votes
1 answer

Generalization of Sum and Product puzzle

I heard from a clever person that for the problem mentioned before: I don't know the two numbers... but now I do a solution exists even if we change 100 to infinity. So the formulation would be ...
klm123's user avatar
  • 16.1k
8 votes
3 answers

The Twins and the Number of Candies

Yveti and Xerni are twins. Their mischievous friend, Cubo, one day decides to give them a riddle. Cubo comes up to them and says, "I have two bags of candies in my bag. The first of you two to guess ...
Mildwood's user avatar
  • 685
8 votes
1 answer

A different extension of the sum and product puzzle

How far down the rabbit hole of not knowing can we go? While working on the generalization of I don't know the two numbers... but now I do, I thought of these two extensions. Both have the same ...
Rob Watts's user avatar
  • 5,946