6 digit number that adds to 23

Question

Find a six-digit number (ABCDEF) in which the second digit is double the first, the third digit is one less than the fourth, the fifth digit is one less than the second digit, the last digit is two less than the fifth digit, and the sum of the digits is 23.

Answer 1

So, the digits can be represented by(assuming that A is the "first" digit.:

A.2A.D-1.D.2A-1.2A-3

The sum of those digits is 23, so 7A-5+2D = 23, or 7A+2D=28. The key is that A and D must be whole numbers between 0 and 9, so try some values for A and see if you can get D to be a whole number. For example if A = 1, then 2D = 21, D=10.5.so rule out A=1. Try A = 2. D=7, seems to work! Go from there.

Answer 2

B = 2A

C = D - 1

E = B - 1, E = 2A - 1

F = E - 2, F = 2A - 1 - 2

Four of the six can be expressed in terms of A. C and D are related only to each other.