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Q.

A person forgets his 4-digit ATM pin code . But he remember that in the code all digits are different, the greatest digit is 7 and the sum of the first two digits is equal to the sum of last two digits. Then the maximum number of trials necessary to obtain the correct code is

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answer is 72.

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Detailed Solution

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Let the 4 digit be abcd Given the a + b = c + d
And one of the number must be 7
0, 1, 2, 3, 4, 5, 6, 7
Let a + b = c + d = $λ$
Sum 7 → 07,16,25,34
Sum 8 → 17,26,35
Sum 9 → 27,36,45
Sum10 $\to$ 37,46
Sum11 → 47,56
$3_{C_{1}} \times 8 + 2_{C_{2}} \times 8 + 2_{C_{1}} \times 8 + 8 + 8 = 72$

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