# Generating 9-Flips

Generating 9-Flips

A 9-flip is a number that when multiplied by 9 has its digits reversed (e.g. ). This Demonstration shows and counts all 9-flips for numbers with 1 to 30 digits.

1089×9=9801

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. is in the middle of and ), while non-straddlers can be split into two 9-flips (e.g. ). The number of 9-flips with an even number of digits () (as well as those with an odd number of digits) forms a Fibonacci sequence and obeys the recurrence relation =+.

109989

10891099891089

109989×9=989901

109989109989

f

2n

f

2n

f

2(n-1)

f

2(n-2)