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Thursday, April 09, 2020

Opening the lock

(this was supposed to be posted yesterday but went to drafts)

This has been going around, and someone asked for help with it, so I've laid out my thought process to solve this below:



Clue 1) 682 - one digit is right and in its place

So it's 6??, ?8? or ??2
Only 6, 8 or 2 can be in the number (assumption: "one" here means "one and only one" - similar assumption applies below)

Clue 2) 614 - one digit is right but in the wrong place

So the full number contains either 6, 1 or 4 but not the other 2
With 1) we know it can't be 6

Possible numbers: 0, 1, 2, 3, 4, 5, 7, 8, 9

Clue 3) 206 - two digits are right but both are in the wrong place
We know it cannot be 6. So the number contains 2 and 0

Possible numbers: 0, 1, 2, 3, 4, 5, 7, 8, 9
Definite numbers: 0, 2

Clue 4) 738 - all digits are wrong

Possible numbers: 0, 1, 2, 4, 5, 9
Definite numbers: 0, 2

From 1), we know it ends with 2
So the number is ??2

From 3) we know the middle number cannot be 0
So the number is 0?2

Possible numbers to fill the gap: 1, 4, 5, 9
From 2) we know it's 1 or 4 but also that the centre number cannot be 1

So it's 042

Clue 5) 380 - one digit is right but in the wrong place

This seems unnecessary
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