Find a four digit number that you can multiply by 4 and get a number with the original digits in reverse order?

Original number is 1000a + 100 b + 10c + d, and a must be 2, If it were 3 or more then multiplying be 4 would give a 5-digit number, and it can't be 1 because it is the units figure in the multiplied number and 1 can't be the last digit in a multiple of 4.

Similarly d must be 3 or 8 to give a number ending in 2 when multiplied by 4,and can't be 3 'cos no multiple of 4 ends in a 3...

Four times original is 4000a + 400b + 40c +4d which equals 1000d + 100c + 10b + a

so 3999a + 390b = 60c + 996d which simplifies to

1333a + 130b = 20c + 332d.

a = 2, d = 8, then 20c - 130b = 2666 - 2656.

20c - 130b = 10 so c = 7 and b = 1

The original number is 2178 (x 4 = 8712)

Whew!