The digits 1 to 9 are arranged in three rows in such a way that each row contains three digits, and the…
The digits 1 to 9 are arranged in three rows in such a way that each row contains three digits, and the number formed in the second row is twice the number formed in the first row; and the number formed in the third row is thrice the number formed in the first row. Repetition of digits is not allowed. If only three of the four digits 2, 3, 7 and 9 are allowed to use in the first row, how many such combinations are possible to be arranged in the three rows?
4
3
2
1
Solution
The first digit of the first row cannot be 7 or 9 (else thrice gives a 4-digit number), so it is 2 or 3. Checking all valid three-digit numbers formed from 2, 3, 7, 9, only 273 (546, 819) and 327 (654, 981) yield a complete arrangement using digits 1-9 without repetition. Hence two combinations are possible.