There is a safe with a 5 digit Number lock. The 4th digit is 4 greater than second digit, while 3rd digit is 3 less than 2nd digit. The 1st digit is thrice the last digit. There are 3 pairs whose sum is 11. Find the number ?
If you set the digits to abcde, where a thru e are integers between 0 and 9, you can immediately get (from the clues) that c can only be 1 or 2, because if it were any greater than 2 this would result in d > 9, out of our range... and thus d ε {8,9}. Also, b ε {4,5} so you have two possibilities there:
(1) c = 1, d = 8, and b = 4 (2) c = 2, d = 9, and b = 5
Doing the same thing with the other two digits (a, e) you get three possibilities:
(1) e = 1, a = 3 (2) e = 2, a = 6 (3) e = 3, a = 9
Using the clue that three pairs add to 11, the only combination from the first group with the second group that gives you these three pairs (whose sums are 11) would be (2) from the first group and (2) from the second group, i.e.
c = 2, d = 9, b = 5 and a = 6, e = 2.
Putting these back into the combination results in the answer: 65292.
6 comments:
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65292
I got 65292.
If you set the digits to abcde, where a thru e are integers between 0 and 9, you can immediately get (from the clues) that c can only be 1 or 2, because if it were any greater than 2 this would result in d > 9, out of our range... and thus d ε {8,9}. Also, b ε {4,5} so you have two possibilities there:
(1) c = 1, d = 8, and b = 4
(2) c = 2, d = 9, and b = 5
Doing the same thing with the other two digits (a, e) you get three possibilities:
(1) e = 1, a = 3
(2) e = 2, a = 6
(3) e = 3, a = 9
Using the clue that three pairs add to 11, the only combination from the first group with the second group that gives you these three pairs (whose sums are 11) would be (2) from the first group and (2) from the second group, i.e.
c = 2, d = 9, b = 5 and
a = 6, e = 2.
Putting these back into the combination results in the answer: 65292.
its 65292.......gud question
Rather interesting place you've got here. Thanks for it. I like such themes and everything connected to them. I definitely want to read more soon.
no u all r wrong...
its 9^5/2
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