perplexus.info :: Logic : Wrong Place, Right Place

Wrong Place, Right Place (Posted on 2003-11-17)

One person comes up to another person beside his bike. "Can I use your bike?" he asks. The person by the bike replies, "Only if you figure out the combination to my bike lock, which is made up of 4 different numbers from 1 through 8. You can guess 3 numbers."

He guessed 1235, 4721, and 3862. All three were answered with "One number in the combination is in the wrong place, and another is in the right place. The other two aren't in the combination."

The guesser was puzzled and asked "Is the number divisible by 7?" The person with the bike answered this question and after thinking for a while, the guesser told him the combination. What is the combination?

Submitted by Gamer

Rating: 3.3333 (9 votes)

Solution: (Hide)

First of all, either 1 is in the combo or 2 is in the combo. If both were, only 3 numbers could be in the combo and if neither was there would have to be at least 5 numbers in the combo. The same reasoning can be applied with 2 and 3.

So there are two scenarios to consider. 1 and 3 are in the combo and 2 isn't, or 2 is in the combo and 1 and 3 aren't.

For the first one: there are 2 choices. 1__3 and __31 because if the last spot isn't filled, the 2 in the last number will make the numbers impossible. 1__3 must be 1763 and the __31 must be 7831.

For the second one: 2__5, __25, because _25_ and 52__ is impossible because the 2 is in the other two combinations in another spot. __25 results in 7825 and 2__5 results in 2765.

Since 2765 is the only number divisible by 7 and the other 3 numbers aren't, the number must be divisible by 7 so the guesser could figure it out. This means the combination was 2765.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
answer	K Sengupta	2007-09-05 05:56:25
Solution	Senthil Kumar	2003-11-21 18:04:05
we got this	kimberly	2003-11-21 00:24:21
cool	r	2003-11-20 10:18:58
woops	bex	2003-11-19 17:40:26
solution?	bex	2003-11-19 17:33:38
No Subject	ben	2003-11-19 09:53:11
wow...	Victor Zapana	2003-11-18 20:28:42
re(3): Dear Silver Kinght and Charlie,,,,,	Charlie	2003-11-18 13:24:48
re: Not to belabor this, but.....	SilverKnight	2003-11-18 13:01:18
Not to belabor this, but.....	Dan	2003-11-18 12:53:18
re(5): Dear Silver Kinght and Charlie,,,,,	SilverKnight	2003-11-18 12:21:16
re(4): Dear Silver Kinght and Charlie,,,,,	Dan	2003-11-18 12:16:24
re: Logical (brute force) solution, no programs	SilverKnight	2003-11-18 12:03:04
Logical (brute force) solution, no programs	fwaff	2003-11-18 11:57:59
re(3): Dear Silver Kinght and Charlie,,,,,	SilverKnight	2003-11-18 11:52:10
re(2): Dear Silver Kinght and Charlie,,,,,	Dan	2003-11-18 11:47:12
re: Dear Silver Kinght and Charlie,,,,,	SilverKnight	2003-11-18 11:36:47
Dear Silver Kinght and Charlie,,,,,	Dan	2003-11-18 11:19:12
In Basic	Charlie	2003-11-18 09:40:19
Solution - the original problem is fine as it is!	SilverKnight	2003-11-18 08:19:40
Here is a corrected version of the original problem.	Dan	2003-11-18 04:20:44
desperate	Lee	2003-11-18 02:44:04
What do I do	Jeff	2003-11-17 21:07:25
re(5): hm...	Victor Zapana	2003-11-17 17:25:54
re(4): hm...	Victor Zapana	2003-11-17 17:21:57
re(3): hm...	SilverKnight	2003-11-17 17:20:01
re(2): hm...	Victor Zapana	2003-11-17 17:08:35
re: hm...	SilverKnight	2003-11-17 16:59:33
hm...	Victor Zapana	2003-11-17 16:56:02
re(2): ahh...	Victor Zapana	2003-11-17 16:51:41
re: ahh...	Gamer	2003-11-17 16:48:01
ahh...	Victor Zapana	2003-11-17 16:44:28
re: Don't comment on this yet!	SilverKnight	2003-11-17 15:53:39
Don't comment on this yet!	Gamer	2003-11-17 14:50:58

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