Triplets

06 May 2022

In a game show, contestants are given a number. If any three digits in the number are the same, they can be removed.

Contestants can increase or decrease a digit in the number by the click of a button. They are required to remove all digits in the number.

For instance, given the number 9 4 3 6 2 7 they could remove all digits as follows:

In that example, $5 + 13 = 18$ clicks are used to remove all digits. But you could have done it with fewer clicks.

What is the smallest number of clicks required to remove all digits in the following number?

\[\textbf{(a)}\ 6\qquad\textbf{(b)}\ 7\qquad\textbf{(c)}\ 8\qquad\textbf{(d)}\ 9\qquad\textbf{(e)}\ 10\]

Click to show my answer

6