There is a safe with a 5 digit number as the key. The 4th digit is 4 greater than
the second digit, while the 3rd digit is 3 less than the 2nd digit. The 1st digit is
thrice the last digit. There are 3 pairs whose sum is 11.
Find the number.
Answer
65292
As per given conditions, there are three possible combinations for 2nd, 3rd and
4th digits. They are (3, 0, 7) or (4, 1, 8) or (5, 2, 9)
It is given that there are 3 pairs whose sum is 11. All possible pairs are (2, 9), (3,
8), (4, 7), (5, 6). Now required number is 5 digit number and it contains 3 pairs of
11. So it must not be having 0 and 1 in it. Hence, the only possible combination
for 2nd, 3rd and 4th digits is (5, 2, 9)
Also, 1st digit is thrice the last digit. The possible combinations are (3, 1), (6, 2)
and (9, 3), out of which only (6, 2) with (5, 2, 9) gives 3 pairs of 11. Hence, the
answer is 65292.
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