(Bababibi) Try This

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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 trial-and-error 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