MathDB

Andy wishes to open an electronic lock with a keypad containing all digits from

0

9

. He knows that the password registered in the system is

2469

. Unfortunately, he is also aware that exactly two different buttons (but he does not know which ones)

\underline{a}

and

\underline{b}

on the keypad are broken

-

when

\underline{a}

is pressed the digit

b

is registered in the system, and when

\underline{b}

is pressed the digit

a

is registered in the system. Find the least number of attempts Andy needs to surely be able to open the lock.
Proposed by Andrew Wen

Problem Statement