Count Transformations (Discussion)

1. MaxymDvali_2012•Oct 20, 2025, 7:32 AM

   why in the editorial there are 4s? like shouldnt it just be 2s and 1s? help plz, thx

   1. MathModel•Oct 25, 2025, 2:41 PM•edited

      MaxymDvali_2012

      We use $\text{choices}[i]$ to represent the choices for digit $i$ , let's consider digit-by-digit

      $0$ : we only can have it as $0$ so we've only single choice

      $1$ : we can multiply by $2$ three times then we've \{1,2,4,8\} which means four choices.

      $2$ : we can multiply by $2$ two times and divide once then we've \{1,2,4,8\} which means four choices.

      $3$ : we can multiply by $2$ once then $\{3,6\}$ which means we've two choices

      $4$ : we can multiply by $2$ once and divide twice then we've \{1,2,4,8\} which means four choices.

      $5$ : we only have it as a choice

      $6$ : we can divide once by $2$ then we've $\{6,3\}$ which means two choices

      $7$ : we only have it as a choice

      $8$ : we can divide three times

      $9$ : we only have it as a choice

      putting it all gives

      \text{choices}=[1,4,4,2,4,1,2,1,4,1]