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Help a man to recover his PIN number?

0 votes
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A man forget his 6 digits PIN number, but fortunately he remembers the clue for his PIN number.

The n-th digit is the first digit of (product of other digits multiplied by n)
The number is not 000000

If the pin is abcdef, then :

The 1st digit = The first digit of 1×b×c×d×e×f
The 2nd digit = the first digit of 2×a×c×d×e×f
...
The 6th digit = The first digit of 6×a×b×c×d×e

What is his pin number ?

posted Dec 17, 2016 by anonymous

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3 Answers

+1 vote

Finally I had to brute force the answer using a c code as I couldn't figure out the analytical approach to this answer.
It is 529311.
The code is below:
enter image description here

enter image description here

answer Dec 19, 2016 by Tejas Naik
–1 vote

111111 shall be answer.

answer Dec 18, 2016 by Subhash Gupta
There won't be a second digit for the product in the next step.
commented Dec 18, 2016 by Tejas Naik
ie., product is 2 in the next step making 2=b then it will be 3=c and so on which contradicts your initial assumption. Hence further iteration needed.
commented Dec 18, 2016 by Tejas Naik
–1 vote

777777 is one solution.
Just do 1x2x3x4x5x6=720 to match all possibilities

answer Dec 18, 2016 by anonymous
1*7*7*7*7*7 = 16807 and it's first digit is 1 contradicting initial assumption of 7.
commented Dec 19, 2016 by Tejas Naik



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