The guards change over between 10: 16 pm and 10: 25 pm which means the hallway is clear during that time. how many minutes do you have exactly to cross the yard without being noticed?

8 minutes.

Step-by-step explanation:

We have been given that the guards change over between 10:16 pm and 10:25 pm which means the hallway is clear during that time.

We can see that the very first minute to cross the hallway without being noticed will be after 10:16 pm as guards start change over at 10:16 pm.

The very last minute to cross the hallway without being noticed will be before 10:25 pm as guards end change over at 10:25 pm.

So let us count number of minutes between 10:16 pm to 10:25 pm without including 10:16 pm and 10:25 pm.

So these minutes will be: 10:17 pm, 10:18 pm, 10:19 pm, 10:20 pm, 10:21 pm, 10:22 pm, 10:23 pm, 10:24 pm.  

Since given time interval includes 8 minutes, therefore, we have only 8 minutes to cross the yard without being noticed.