Fill in each square on the left with a digit (0 to 9), and fill in each circle with any one of the 4 arithmetic operations $(+, -, \times, \div )$ .

We can get many numbers like:

$\begin{array} { c c c c c }
3 & - & 2 & = & 1 \\
1 & \times & 2 & = & 2 \\
2 & + & 1 & = & 3 \\
1 & + & 3 & = & 4 \\
& & \vdots & & \\
\end{array}$

What is the smallest positive integer that we cannot achieve?

19
23
25
17

**
This section requires Javascript.
**

You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.

since we we can get $17$ as $9+8=17$ , the next smallest number is $19$ since it is a

primewe can not get it by $(\times,\div,-)$ .moreover we can not get it byadditionbecause the greatest number in the set is $9$ in order to get $19$ we must have at least $10$ . so19is the answer .