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Winning Number (Posted on 2013-06-26) Difficulty: 3 of 5
"Dad, what’s this week’s winning lottery number?" asked Chloe.

"Coincidentally," her father replied, "exactly one digit in each of the five columns in the previous six winning numbers on this piece of paper is in the same position as one of the digits in this week’s winning number."

"Thanks, Dad." said Chloe, looking at the numbers over his shoulder. "But I can’t determine the number from that information."

Chloe then showed the same numbers to her mother, which were as follows:
                  
                +---------------+
                | 0  9  9  0  6 |
                | 0  1  6  9  1 |
                | 8  9  6  8  9 |
                | 0  9  6  0  9 |
                | 1  9  6  8  9 |
                | 8  6  8  8  9 | 
                +---------------+
"Your dad’s right." she said, "Exactly one digit in each of the five columns is in the same position as one of the digits in this week’s winning number, which, incidentally, is ...."

"Thanks, Mom," interrupted Chloe, "But now I know what it is."

What is this week’s winning number?

No Solution Yet Submitted by K Sengupta    
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Solution full explanation (spoiler) | Comment 3 of 4 |
(In reply to explanation (spoiler) by Charlie)

The mother is not providing any additional information, unless Chloe somehow showed the mother a different list than the father.  The trick is that all of these digits (0,1,6,8,9) are also digits when upside down.  Chloe showed it to her mother upside down, and upside down her Mother made the same statement as the Father.  Upside down does not give rise to an unambiguous answer, but taking the two together it can be deduced.


The only digit in the 1st column which is upside down in the 5th column is 1 is 1, so the number starts and ends in 1.

The only digit in the 2nd column which is upside down in the 4th column is 6, so 6 is the 2nd digit and 9 (i.e., 6 upside down) is the 4th.

And as for the middle column, the 6, 8 and 9 are all there when inverted, but only 8 is there just once both right side up and upside down.

The full number is therefore 16891. 

Edited on June 27, 2013, 8:52 am
  Posted by Steve Herman on 2013-06-26 15:37:57

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