Question 1096519: If you rotate a sheet of paper by 180 degrees, digits 0, 1, and 8 do not change; 6 becomes a 9; 9 becomes a 6; while other digits lose their meaning. Count all the 7-digit numbers that do not change upon rotation by 180 degrees.
Found 2 solutions by greenestamps, Gentle Phill:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
(1) All the digits must be either 0, 1, or 8.
(2) Since you are rotating the whole 7-digit number 180 degrees and you want to end up with the same number, the 1st and 7th digits must be the same; the 2nd and 6th must be the same, and the 3rd and 5th must be the same. The 4th digit, being in the middle, can be any one of the 3 allowable digits.
...there are 2 choices for the 1st digit (it can't be 0); and then there is only 1 choice for the 7th digit.
...there are 3 choices for the 2nd digit, and then only 1 choice for the 6th.
...There are 3 choices for the 3rd digit, and then only 1 choice for the 5th.
...there are 3 choices for the 4th digit.
The total number of choices, and therefore the number of 7-digit numbers that satisfy the requirements, is
Answer by Gentle Phill(18)  (Show Source):
You can put this solution on YOUR website! #SOLN
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...Let's crack some nuts...
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Collect data..
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Only numbers with 0, 1 and 8 do not oppose the motion.
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Process data..
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Form seven-digit numbers with 0, 1 and 8
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Millions place can take only 2 digits (1 and 8)
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Others (from hundreds of thousand down to unit) can take all 3 each.
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We have:
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[2][3][3][3][3][3][3] nos
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Give out Information..
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558 seven-digit numbers can be rotated half way but remain same.
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#CRACKED
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Your friend,
Francis.
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