New Math Riddle Competition!

  • Thread starter rkastner
  • Start date
  • #1
rkastner
264
38
Just for fun and for community participation, I offer the following riddle. The person who answers first (with complete explanation of how the answer is deduced) wins a free copy of Understanding Our Unseen Reality: Solving Quantum Riddles.

Question: Susie and Paula's teacher gives Susie the sum of two numbers. The teacher gives Paula the product of the same two numbers. Both numbers are greater than or equal to 2. While trying to determine the two numbers, Susie and Paula have the following conversation:

Susie: Paula, I don't know what the numbers are.
Paula: I knew you didn't know, but neither do I.
Susie: In that case, I know the numbers!

What are the numbers?
 
  • Like
Likes Joosh, jackwhirl and Greg Bernhardt

Answers and Replies

  • #2
jackwhirl
234
153
The numbers are 3 and 4.
Susie's sum is 7, which she knows could be the sum of (2 and 5) or (3 and 4), but not which.
Paula's product is 12, which she knows could be the product of (2 and 6) or (3 and 4), but not which.
When Paula admits ignorance, Susie knows the answer because if the numbers were 2 and 5, Paula's product would be 10 with only one solution, 2 and 5.

This is a solution. Is it the only one?
 
Last edited:
  • #3
rkastner
264
38
Thanks! That is the intended answer to the riddle (which was not my own invention). But on further reflection, I believe there is at least one counterexample to the premise of the riddle. That is, it seems to me that (without further restriction on the range of numbers), there are pairs of numbers whose sum and product do not permit Susie to infer with certainty what the numbers are based only on Paula's statement. I leave that out there in case anyone wants to check for themselves.
Meanwhile, Jackwhirl, please contact me privately to let me know where you'd like the book to be sent!
 
  • Like
Likes Greg Bernhardt

Suggested for: New Math Riddle Competition!

  • Last Post
Replies
2
Views
272
  • Last Post
Replies
5
Views
405
  • Last Post
Replies
5
Views
1K
Replies
86
Views
2K
  • Last Post
Replies
4
Views
873
Replies
1
Views
197
  • Last Post
Replies
1
Views
716
Replies
11
Views
182
  • Last Post
Replies
12
Views
687
  • Last Post
Replies
6
Views
516
Top