Question 1153929: where x is a 6 digit number, the sum 1st and 2nd number is 7,the 3rd number equals the first number, the 4th is equal to the 2nd plus 2, the sum of the 4th and 5th number is 8, the 6th number is the square of the 4th number, the sum of the 6 digit is 26,what is the value of x
Found 2 solutions by ramkikk66, greenestamps:
Answer by ramkikk66(644)   (Show Source):
You can put this solution on YOUR website!
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 707264. Solved.
Answer by greenestamps(13209)  (Show Source):
You can put this solution on YOUR website!
Use the clues in an order which gets you to the solution fastest.
The clue that immediately limits the possibilities to only a very small number is the one that says one digit is the square of the other.
The possibilities for single digits are 1 and 1, 2 and 4, or 3 and 9. 1 and 1 is unlikely, so I will ignore it.
(1) the 6th digit is the square of the 4th:
x x x 2 x 4 OR x x x 3 x 9
(2) the 4th digit is the 2nd digit plus 2:
x 0 x 2 x 4 OR x 1 x 3 x 9
(3) the sum of the 4th and 5th digits is 8:
x 0 x 2 6 4 OR x 1 x 3 5 9
(4) the sum of the 1st and 2nd digits is 7:
7 0 x 2 6 4 OR 6 1 x 3 5 9
(5) the 3rd digit is equal to the first:
7 0 7 2 6 4 OR 6 1 6 3 5 9
(6) the sum of the six digits is 26:
7+0+7+2+6+4 = 26 (OK); 6+1+6+3+5+9 = 30 (not OK)
ANSWER: 707264
|
|
|
