The dimension of an array directly depends on the screen size of the device it is being viewed on. The jumping point is of course the iPhone. In many cases, match-three games are played in Portrait mode, so the width of the game board is equal to 320 points (640 pixels on the Retina display and 320 pixels on the iPhone 3GS). As long as touchscreen input is based on direct manipulations with objects on the screen, a game tile should be comfortable to aim and tap. (Systems with non-direct manipulation, which use buttons or a joystick to control the screen pointer, can use smaller tiles and more elements.)
As you remember from Chapter 2, Ergonomics, the optimal minimum size of a touch area is 44 pixels. If we divide 320 points by 44 points, the rounded-up result is 7.3. Hence the optimal number of elements is seven or eight; you can check this out for yourself by looking at any screenshot of the Bejeweled game, which utilizes eight items in a row. Besides the ergonomics...