I wrote this app for my teenage son who has profound learning difficulties and no speech, to entertain him and help with his development. The app is a picture matching game, which displays a picture at the top of the screen and 4 pictures at the bottom of the screen.
I wrote it for the iPad, in Objective-C. It's available, for free, in the iTunes store: https://itunes.apple.com/gb/artist/ian-ellis/id754782887
If you tap the same picture at the bottom of the screen as is displayed at the top of the screen the app plays a success sequence to reward you, before starting over with a new set of pictures.
The app is designed to have minimum clutter on the game screen. There are no other controls on the screen other than the pictures. The app always loads into a settings page. Here you can select the categories of pictures that will be displayed, choose whether to have 2 or 4 pictures to select from (defaults to 2) and record/play/delete personal message that you want played when the correct image is selected. The settings are saved to iOS defaults so that they remain as you set them each time you use it. To change them once playing, simply exit the app & launch it again.
Once you've pressed the Go button the game starts until you exit from the application (I advise that you use the Guided Access option from the Accessibility settings to control exiting from the app).