SOLUTION: If all digits 0,1,2,3,4,5,6,7,8,9 are rotated through a 180 degrees ,the
digits 0,1, and 8 do not change meaning, the digit 6 becomes 9, and 9
becomes 6. The remaining digits los
Algebra ->
Permutations
-> SOLUTION: If all digits 0,1,2,3,4,5,6,7,8,9 are rotated through a 180 degrees ,the
digits 0,1, and 8 do not change meaning, the digit 6 becomes 9, and 9
becomes 6. The remaining digits los
Log On
Question 1146125: If all digits 0,1,2,3,4,5,6,7,8,9 are rotated through a 180 degrees ,the
digits 0,1, and 8 do not change meaning, the digit 6 becomes 9, and 9
becomes 6. The remaining digits lose their meaning. a palidium is a positive
whole number that remains the same after a 180 degree rotation(for example, 1691 or 8008). How many numbers between 1000 and 9999(inclusive) are
palidiums? Answer by Edwin McCravy(20054) (Show Source):
First we see how many ways we can have the outer two digits.
They can be
1 _ _ 1
8 _ _ 8
6 _ _ 9
9 _ _ 6
So we can pick the outer digits 4 different ways.
Next we see how many ways we can have the middle two digits.
They can be
_ 0 0 _
_ 1 1 _
_ 8 8 _
_ 6 9 _
_ 9 6 _
So we can pick middle two digits 5 different ways.
So for each of the 4 ways we can pick the outer two digit,
we can pick the inner two digits 5 ways.
So there are 4×5 or 20 ways to have a palidum.
Here are all 20 palidia:
1. 1 0 0 1
2. 8 0 0 8
3. 6 0 0 9
4. 9 0 0 6
5. 1 1 1 1
6. 8 1 1 8
7. 6 1 1 9
8. 9 1 1 6
9. 1 8 8 1
10. 8 8 8 8
11. 6 8 8 9
12. 9 8 8 6
13. 1 6 9 1
14. 8 6 9 8
15. 6 6 9 9
16. 9 6 9 6
17. 1 9 6 1
18. 8 9 6 8
19. 6 9 6 9
20. 9 9 6 6
Edwin
