Question 106472
Call the digits d1, d2, d3, d4, d5, and d6


The relationships described are:


d1 = d2 - 1
d2 = d3 - 1
d4 = d5 - 1
d5 = d6 - 1
d2 = d4 + d5 + d6
d3 = d2 + d4


Giving us 6 linear equations in 6 variables.


Rearrange each equation so that you have an expression set equal to zero


1) d1 - d2 + 1 = 0
2) d2 - d3 + 1 = 0
3) d2 - d4 - d5 - d6 = 0
4) -d2 + d3 -d4 = 0
5) d4 - d5 + 1 = 0
6) d5 - d6 + 1 = 0


Add equation 4) to equation 2), resulting in


0d2 + 0d3 - d4 + 1 = 0, which reduces to
d4 = 1


Substituting d4 in equation 5), d5 = 2
Substituting d5 in equation 6), d6 = 3
Substituting d4, d5, and d6 in equation 3), d2 = 6
Substituting d2 in equation 1), d1 = 5
Substituting d2 in equation 2), d3 = 7


Hence the number is 567123.


Check,


5 is one less than 6.
6 is one less than 7.
1 is one less than 2.
2 is one less than 3.
6 is equal to 1 + 2 + 3
7 is equal to 6 + 1