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0,1,2,5,8,11,69,96 are Strobogrammatic numbers.
We call a Strobogrammatic numbers if:
When it is typed on a calculator, and the calculator is spun 180 degrees, the number visually looks the same.
How many Strobogrammatic numbers are there from 0 to 99999?
This is a no-computer puzzle; only the first right answer with explanation will be accepted.
assumption: we can not usually have leading zeroes on a calculator, they are usually stripped.
the spinnable digits are 0, 1, 2, 5, (6/9), and 8
For 1 digit
Pos 1: we can have any of the five non-paired options (0 is not stripped in this one instance, as 0 is displayed on the calculator)
Total: 5
For 2 digits:
Pos 1: we can have any of the six non-zero spinnable digits
Pos 2: we can only have the inverse digit of pos 1
Total 6x1 = 6
For 3 digits:
Pos 1: we can have any of the six non-zero spinnable digits
Pos 2: we can have any of the five self-referential spinnable digits
Pos 3: we can only have the inverse digit of pos 1
Total 6x5x1 = 30
For 4 digits:
Pos 1: we can have any of the six non-zero spinnable digits
Pos 2: we can have any of the seven spinnable digits
Pos 3: we can only have the inverse digit of pos 2
Pos 4: we can only have the inverse digit of pos 1
Total: 6x7x1x1 = 42
For 5 digits
Pos 1: we can have any of the six non-zero spinnable digits
Pos 2: we can have any of the seven spinnable digits
Pos 3: we can have any of the five self-referential spinnable digits
Pos 4: we can only have the inverse digit of pos 2
Pos 5: we can only have the inverse digit of pos 1
Total: 6x7x5x1x1 = 210
Thus all spinnable numbers from 0 to 99999 is the sum:
5+6+30+42+210 = 293
So:
There are 293 spinnable numbers between 0 and 99999
Late, but different approach.
Self spinnable numbers: 0, 1, 2, 5, 8
Spinnable pair: 6 and 9
1 digit (5)
All the self spinnable numbers
2 digits (6)
Self spinnable: 11, 22, 55, 88
Pair spinnable: 69, 96
3 digits (30)
Self spinnable: 1x1, 2x2, 5x5, 8x8
Pair spinnable: 6x9, 9x6
One digit spinnable numbers go intox
So, 6 x 5 = 30
4 digits (42)
Self spinnable: 1xx1, 2xx2, 5xx5, 8xx8
Pair spinnable: 6xx9, 9xx6
Two digits spinnable numbers (including 00) go intoxx
So, 6 x 7 = 42
5 digits (210)
Self spinnable: 1xxx1, 2xxx2, 5xxx5, 8xxx8
Pair spinnable: 6xxx9, 9xxx6
Three digits spinnable numbers (including 000) go intoxxx
So, 6 x (7 x 5) = 210
And, 5 + 6 + 30 + 42 + 210 is 293.
including 000 in your 5 digits calculation should really be including 0x0, otherwise your calculation would be 6 x (30 + 1) instead of 6 x ((6+1) x 5).
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