WOLFRAM|DEMONSTRATIONS PROJECT

Generating 9-Flips

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number of digits
2
number of digits
2
number of 9-flips
0
Null
A 9-flip is a number that when multiplied by 9 has its digits reversed (e.g.
1089×9=9801
). This Demonstration shows and counts all 9-flips for numbers with 1 to 30 digits.
9-flips with an even number of digits can be divided into two types: straddlers (shown in red and dark red) and non-straddlers (shown in blue and dark blue).
Straddlers have a central block in the middle that is a 9-flip (e.g.
109989
is in the middle of
10891099891089
and
109989×9=989901
), while non-straddlers can be split into two 9-flips (e.g.
109989109989
). The number of 9-flips with an even number of digits (
f
2n
) (as well as those with an odd number of digits) forms a Fibonacci sequence and obeys the recurrence relation
f
2n
=
f
2(n-1)
+
f
2(n-2)
.