After an automatic update, my iPad restarted and now requires a passcode

I'd say that if you're unable to follow the steps below, because you don't have another computer running iTunes, you may have to take it to an Apple Store to have them perform a factory reset.

1. Open iTunes
2. Sign into iTunes on your computer. As a security measure, you will need your Apple ID and password to reset the iPad.
3. Start Recovery Mode
4. Recovery mode is what directs iTunes to either update or erase the iPad. You need to start this process before connecting the iPad to your computer. Because you'll need to hold down a button or two while connecting the iPad, connect its cable to your computer first, and then you can more easily connect the iPad once recovery mode has started. The process varies a bit, depending on which iPad model you have.
5. iPad with Home button: Hold down the Top or Side button until the Power Off slider appears on the screen. Drag the slider to turn off the iPad. Then hold down the Home button while connecting the iPad to your computer. Release the Home button only after the recovery mode screen appears.
6. iPad with Face ID: Press and hold the Top button and one of the volume buttons until you see the Power Off slider. Drag the slider to turn off your iPad. Continue holding down the Top button and connect your device to the computer. You can release the Top button after you see the recover-mode screen.
7. Restore the iPad to Factory Settings
8. Once the recover-mode screen appears on the iPad, iTunes should automatically launch on your computer. It will give you the option to restore or update the iPad. Click Restore. Restoring the iPad can take several minutes.

How to Hard Reset an iPad

If your iPad is frozen, preventing you from unlocking it with your passcode, or if it doesn't recognize your taps or the slider doesn't work, a hard reset/hard reboot of your iPad will often do the trick. This forces the iPad to turn off and on, flushing its memory clean. A hard reset, however, does not delete your data.

Press the Home button and the On/Off button at the same time. Keep holding the buttons down until after the screen turns black and the iPad starts up again. When the Apple logo appears on the screen, release the buttons.

You should now be able to access the iPad, provided you know the passcode. If you still need to erase the data and restore it to factory settings, you can do that with iTunes or from the iPad settings.

How to Erase iPad From Settings

If you are now able to open your iPad, you can erase all of your data and return it to its factory default settings without connecting it to a computer.

1. Ensure that your iPad is charged, or connect it to a power source. 
2. Open Settings; select General and then select Reset. 
3. Select Erase All Content and Settings. Enter your passcode or your Apple ID password if prompted. This password is the one that's associated with your email address and used to access the App Store or iCloud.
4. Confirm that you want to erase everything on your iPad. 

After several minutes, the iPad will restart, giving you the same welcome screen as when you purchased it.

If you have an iPhone, did you try entering that passcode?

maybe have a look at this page.

If you forgot the passcode on your iPad

Have you tried entering the default passcodes; such as:

•  123456
•  000000
•  1234
•  0000

How have you been unlocking your ipad? Touch ID? Face ID?

i understood that the iPad never had a passcode. i gave you that link because those steps for "if you forgot" can sometimes help in a situation such as yours.