Question

You need to turn the four digits of a number lock to the right combination to unlock it. Each digit on the lock can be
turned forward or backwards.

In the image here, 2719 are the present digits on the lock. 7 can be turned forward to 8, or backward to 6. If you turn 9
forward, it circularly goes to 0. Likewise, if you turn 0 backwards, you circle back to 9.
Question:
What is the minimum number of turns to unlock the number lock if the present digits are 2719 and the key combination
to open the lock is 4383?
19
21
17
12
13​

Answer 1

Given : turn the four digits of a number lock to the right combination to unlock it.  Each digit on the lock can be turned forward or backwards.

Digits are from 0 to 9 in circular

To Find : minimum number of turns to unlock the number lock if the present digits are 2719 and the key combination to open the lock is 4383

19

21

17

12

13​

Solution:

Current combination is  2719

key combination to open the lock is 4383

2  7    1    9

4  3    8   3

There are 10 turns to comeback at same position

Hence if turns required in one direction are more than 5 than choose other direction

2 to 4  => 2 turns  forward  

7 to  3  => 6 turns forward so  4 turns backward is better option

1 to  8  => 7 turns forward so  3 turns backward is better option

9  to 3  => 4  turns forward  

Best option is :

2 to 4  => 2 turns  forward  

7 to  3  =>  4 turns backward  

1 to  8  =>  3 turns backward

9  to 3  => 4  turns forward  

2 + 4 + 3 + 4  = 13

13 is the minimum number of turns to unlock the number lock if the present digits are 2719 and the key combination to open the lock is 4383

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