Question

Using the 0,1,6,8, and 9, write down all the possible three-digit numbers that have rotational symmetry. the digits can be used more then once

Answer 1

Assuming 1 is written rotationally symmetrical, using 0,1,6,8,9 to make numbers that have a degree of symmetry of 2 (i.e. 180 degrees), we can say

one digit numbers: 0,1,8

two digit numbers: 11, 69, 96

(18 becomes 81, so not admissible, similarly for 19, 91,16,61, etc)

(00 is not considered generally as a two-digit number)

three digit numbers:

(000, 010, 080 are not considered generally as a three-digit number)

101, 609, 808, 906,

replace the middle digit successively by 1 and 8 gives

111, 619, 818, 916,

181, 689, 888, 986

for a total of 12 numbers