Placing operators among digits

MediumCombinatorics~4m

How many arithmetic expressions can be formed from the string $123456789$ (digits kept in order) by choosing, in each of the $8$ gaps between consecutive digits, to either concatenate the digits, insert a $+$ , or insert a $\times$ ? (For example, $1 + 23 \times 4 + \dots$ )

Show hints (2)+

There are $8$ gaps between the $9$ digits.
Each gap has $3$ independent choices (join, $+$ , $\times$ ): $3^8$ .

Answer

Reveal answer →

6561

Create a free account to see the full worked solution and track your progress.

Create a free account

Interview format: Market Maker, Hedge Fund Quant

Placing operators among digits

Answer

Related questions