Question 1153929
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Let us call the 6 digits D1 to D6.

Given data.
1) D1 + D2 = 7
2) D3  = D1
3) D4 = D2 + 2 
4) D4 + D5 = 8
5) D6 = square of D4
6) Sum of D1+D2+D3+D4+D5+D6 = 26

From #5, D6 is a single-digit square number. So it can only be 0,1,4 or 9. Correspondingly, D4 is 0, 1, 2 or 3.

From #3, D4 = D2 + 2. So D4 cannot be 0 or 1. D4 is either 2 or 3

Let's check both the cases

If D4 = 2, 
D2 = 0 (from #3) and 
D1 = 7 - 0 = 7 (from #1), 
D3 = 7 (from #2), 
D5 = 6 (from #4) and 
D6 = 4 (from #5)
Num is 707264. Sum of digits = 26 which matches.


To confirm, let's try the other possibility also.

If D4 = 3, 
D2 = 1(from #3) and 
D1 = 7 - 1 = 6 (from #1), 
D3 = 6 (from #2), 
D5 = 5(from #4) and 
D6 = 9 (from #5)

Num is 616359. Sum of digits = 30 which does not match.


Hence the answer is <b>707264</b>. Solved.

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