Question

Password of lock is a 5-digit number. A little information about it is as follows:

· The fourth digit is 4 greater than the second digit.
· The third digit is 3 less than the second digit.
· The first digit is thrice the last digit.
· There are 3 pairs of digits whose sum is 11.
Password=?

Answer 1

Can't we let the 5 digits be abcde and then..solve..like
d=4+b
c=3-b..
c+d=7...etc?

Answer 2

abcde
according the question,
d=b+4
c=b-3
a=3e
So, the lock becomes
(3e)b(b-3)(b+4)e

Answer 3

haha!

Answer 4

Also, 3<=b<=5

Answer 5

0<=e<=3

Answer 6

d=4+b
c=b-3
this gives..d-c=7

Answer 7

How to utilize this?
There are 3 pairs of digits whose sum is 11.

Answer 8

since 2nd digit can only have values from 3 and 5 for c and d to have values between 0 and 9 ,
we see there are only 3 possible combos for 2nd, 3rd and 4th digits.
(3, 0, 7)
(4, 1, 8)
(5, 2, 9)
It is given that there are 3 pairs whose sum is 11.
11= 2+ 9= 3+ 8=4+ 7=5+ 6.
so we can not have a 0 or 1 there..
hence the ans must be _529_

1st digit=3* last digit.
The possible combinations are (3, 1), (6, 2) and (9, 3)
hit and trial shows only 6 and 2 fir it for 3 pairs summing to 11
hence ans=65292.
please confirm..

Answer 9

yes its correct

Answer 10

phew!

Answer 11

bingo!