Author 
Message 
bababibi (Frankbubu)
 Posted on Friday, June 10, 2005  11:25 am:  
I have chosen two different numbers greater than N but less than M. I tell their sum to Mr. S and their product to Ms. P. The following conversation ensues: Mr. S: I cannot determine the two numbers. Ms. P: I cannot determine the two numbers either. Mr. S: I still cannot determine the two numbers. Ms. P: Now I can determine the two numbers. Mr. S: Now I can determine the two numbers also. Find the greatest value of M for which this puzzle has a unique solution, for N=1 
Martin Schwenk (Trickymartin)
 Posted on Friday, June 10, 2005  1:24 pm:  
Ok let's do this step by step, as I have no idea of how to find the greatest M otherwise. I call the numbers x and y. Obviously, M must be 4 or greater. M=4. a,b e {2,3}. Trivial. Mr. S would have known from the start. M=5. a,b e {2,3,4}. Mr. S would have known from the start, as any sum is unique. M=6. a,b e {2,3,4,5}. The only ambigue sum is 7. knowing that, Ms. P would have known x and y after Mr. S' first statement. 
Martin Schwenk (Trickymartin)
 Posted on Friday, June 10, 2005  1:30 pm:  
M=7. a,b e {2,3,4,5,6}. (x+y) e {7,8,9} (otherwise Ms. S would have known). a1) S=7: x=2,y=5 > P=10. a2) x=3,y=4 > P=12 b1) S=8: x=2,y=6 > P=12. b2) x=3,y=5 > P=15 c1) S=9: x=3,y=6 > P=18. c2) x=4,y=5 > P=20 It has to be P=12, otherwise Mr. P would have known. Ms. S now can deduce P=12. So she can figure out x and y. I hope there is a solution at all? 
Martin Schwenk (Trickymartin)
 Posted on Friday, June 10, 2005  1:35 pm:  
M=8. a,b e {2,3,4,5,6,7}. (x+y) e {7,8,9,10,11} (otherwise Ms. S would have known). a1) S=7: x=2,y=5 > P=10. a2) x=3,y=4 > P=12 b1) S=8: x=2,y=6 > P=12. b2) x=3,y=5 > P=15 c1) S=9: x=3,y=6 > P=18. c2) x=4,y=5 > P=20. c3) x=2,y=7 > P=14 d1) S=10: x=3,y=7 > P=21. d2) x=4,y=6 > P=24 e1) S=11: x=4,y=7 > P=28. e2) x=5,y=6 > P=30 Again this leaves only P=12, So Mr. S would have known it after Ms. P's first statement. 
Martin Schwenk (Trickymartin)
 Posted on Friday, June 10, 2005  1:47 pm:  
Whoops. "a,b e {..." was supposed to read "x,y" e {...}} M=9. x,y e {2,3,4,5,6,7,8}. (x+y) e {7,8,9,10,11} (otherwise Ms. S would have known). a1) S=7: x=2,y=5 > P=10. a2) x=3,y=4 > P=12 b1) S=8: x=2,y=6 > P=12. b2) x=3,y=5 > P=15 c1) S=9: x=3,y=6 > P=18. c2) x=4,y=5 > P=20. c3) x=2,y=7 > P=14 d1) S=10: x=3,y=7 > P=21. d2) x=4,y=6 > P=24. d3) x=2,y=8 > P=16 e1) S=11: x=4,y=7 > P=28. e2) x=5,y=6 > P=30. e3) x=3,y=8 > P=24 As Ms. P doen't know it, P e {12,24}. With that information, Mr. S can deduce x and y. I hope there's another way to solve this as trialanderror proves not to be too fruitful... 
bababibi (Frankbubu)
 Posted on Friday, June 10, 2005  2:54 pm:  
martin is there a easy way to get around this problem. i've been banging my head. 
Mezzoforte (Mezzoforte)
 Posted on Friday, June 10, 2005  3:22 pm:  
Do they tell each other the number you told each of them? 
bababibi (Frankbubu)
 Posted on Friday, June 10, 2005  3:29 pm:  
no it can't be. 
Shawn Franchi (Doctapeppa)
 Posted on Friday, June 10, 2005  8:57 pm:  
Simple. N=1, M=50000 You pick 1.1 and 413752 You tell Mr. S that the sum is 413753.1. You tell Ms. P that their product is 455127.2. When Ms. P finds out that Mr. S could not determine the numbers even after Ms. P said she couldn't determine the numbers, she realizes what the numbers are. When Mr. S knows that Ms. P figured it out, he knows what the numbers must be, as well. UNIQUE 
Torgeir Apeland (Abc)
 Posted on Sunday, June 12, 2005  11:53 am:  
Do mr. S and mr. P know N? M? Are the two numbers picked, and M, limited to integers? And, if so, do S and P know this? 
Martin Schwenk (Trickymartin)
 Posted on Sunday, June 12, 2005  12:22 pm:  
Does this have to work for every two numbers picked, for a given M? or just for one specific pair? 
Martin Schwenk (Trickymartin)
 Posted on Sunday, June 12, 2005  12:24 pm:  
@Shawn: I think it is given the numbers must be whole numbers. 
Shawn Franchi (Doctapeppa)
 Posted on Monday, June 13, 2005  3:00 am:  
Where? I don't see it given anywhere. 
Martin Schwenk (Trickymartin)
 Posted on Monday, June 13, 2005  9:14 am:  
Anyway, your example doesn't work. How should they ever realize the numbers? 
Shawn Franchi (Doctapeppa)
 Posted on Tuesday, June 14, 2005  3:56 pm:  
The same way they would with any other numbers 
Moderator Feenwelt (Dietmar)
 Posted on Monday, July 04, 2005  7:49 pm:  
Spoiler 
Mezzoforte (Mezzoforte)
 Posted on Tuesday, July 05, 2005  3:12 pm:  
What's the spoiler? 
Moderator Feenwelt (Dietmar)
 Posted on Tuesday, July 05, 2005  5:20 pm:  
Sorry? Do you mean: "What is a spoiler?" or do you mean "Why is here a spoiler?"??? slightly confused 
Mezzoforte (Mezzoforte)
 Posted on Wednesday, July 06, 2005  3:28 pm:  
the latter 
Moderator Feenwelt (Dietmar)
 Posted on Thursday, July 07, 2005  4:56 pm:  
First: this is not a lateral. Second: The puzzle seems solved, Martin posted an answer. Third: Bababibi hasn't posted anything else since June 10th. To me it looks as if nothing more is going to happen here. 
Mezzoforte (Mezzoforte)
 Posted on Tuesday, July 12, 2005  10:08 pm:  
Ok then. 
Christopher Anderson (Cazo97)
 Posted on Monday, August 01, 2005  8:59 pm:  
3 and 4 
Christopher Anderson (Cazo97)
 Posted on Monday, August 01, 2005  9:01 pm:  
are the two numbers different? 
Christopher Anderson (Cazo97)
 Posted on Monday, August 01, 2005  9:03 pm:  
nevermind, it's in the puzzle 
