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.
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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.
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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