A person forgets his 4-digit ATM pin code. But he remembers that in the code all the digits are different, the greatest digit is 7 and the sum of the first two digits is equal to the sum of the last two digits. Then the maximum number of trials necessary to obtain the correct code is________.
Text Solution
Verified by Experts72
(72)
Let the 4-digit pin be abed
Now given sum of first two is equal to last two, so a + b = c + d
And number available are 0, 1, 2, 3, 4, 5, 6, 7
Now Let a + b = c + d = 
Also the greatest digit that he has used is 7
So, a + b = c + d = 
7
Now taking all cases starting from 
= 7 we get,
= 7, (a, b) 
(0, 7) or (7,0), then (c, d) 
(l, 6),(2, 5),(3,4),(4,3),(5, 2),(6,1) and vice-versa, so 2 x 12 = 24 numbers
= 8, (a, b) 
(1, 7) or (7,1), then (c, d) 
(2, 6),(3, 5),(6, 2),(5,3) and vice versa so total 2 x 8 = 16 numbers,
= 9, (a, b) 
(2, 7) or (7, 2) then (c, d) 
(3, 6),(4, 5),(5,4),(6,3) and vice versa, so total 2 x 8 = 16 numbers,
= 10, (a, b) 
(3, 7),(7, 3), so (c, d) 
(6, 4),(4, 6) 
8 numbers
= 11, (a, b) 
(4, 7),(7, 4), so (c, d) 
(6, 5),(5, 6) 
8 numbers
= 12, 13 & 14 are not possible,
So, Total numbers = 24 + 16 + 16 + 8 + 8 = 72
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