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6-digit number

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6-digit number

by Innsmouth » Thu Mar 26, 2009 9:33 am
i hope that question does not exist on the forum . i've searched for it but i couldn't find. please help me about this problem it's driving me crazy!!


6 Digit Number
(2) We have a six digit number with no repeating digits. To find this number the following predictions are made.

123456, 234567, 345678, 456789, 567012, 654321, 765432, 876543, 987654

In each prediction only one digit is placed correctly. Find the number.

thanks for your interest from this moment..
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Re: 6-digit number

by Stuart@KaplanGMAT » Thu Mar 26, 2009 11:50 am
Innsmouth wrote:i hope that question does not exist on the forum . i've searched for it but i couldn't find. please help me about this problem it's driving me crazy!!


6 Digit Number
(2) We have a six digit number with no repeating digits. To find this number the following predictions are made.

123456, 234567, 345678, 456789, 567012, 654321, 765432, 876543, 987654

In each prediction only one digit is placed correctly. Find the number.

thanks for your interest from this moment..
I'm guessing the reason you couldn't find the question anywhere is that it's not a GMAT (or GMAT style) question. No GMAT question has ever started with the phrase "We have a ... " and every GMAT question has answer choices.

By far the quickest way to solve this question on a multiple choice exam would be via backsolving, i.e. working backwards from the choices and finding one that matches up with exactly 1 digit from each prediction. With answer choices, this problem could easily be solved in under 1 minute.
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by Ian Stewart » Thu Mar 26, 2009 1:39 pm
174682 works here, though I don't see any especially fast way to find it. It's helpful to notice that we have nine predictions, and if one digit is correct in each, then the answer must have three digits which appear in two predictions, and three digits which appear in one prediction. I then noticed that the first and last digits are paired in each prediction except when the last digit is 2 (by paired, I mean that when the first digit is 1, the last digit is 6, and when the first digit is 6, the last digit is 1), and anticipating that this restriction would be what would prevent most possibilities from working, I then settled on 2 for the last digit, and found the remaining digits through a process of elimination.

That certainly took more than two minutes, and while there may well be a faster way to get to the answer directly, I don't see it at a glance. If it were a real GMAT problem (it is not at all similar to any GMAT problem I've ever seen), and if it had answer choices, then, as Stuart points out, it would be straightforward to answer.
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