The letters are written on arcs which rotate when a letter on the arc is clicked. The arcs are of different heights, and the appearance at a position is that of the letter in that position, if any, of the highest arc. Clicking on the tab next to a letter on an arc moves the arc. Depending on its height one end may obscure a letter on a lower arc or go under an arc on a higher level. HORSES is on the arc at highest level and therefore never disappears. The arcs below have the letter sequences ELEPHANTS, COWS and the single letter R. The words have no significance. You merely caught me making letter sequences at random with no goal of achieving randomness.
A program might be given the concept of height and one object obscuring another. There is a problem of doing this fairly.
Tom Costello pointed out that if the letter displayed from a column were not the highest but were the earliest in alphabetical order, the puzzle would be much harder - at least for people.
I hope machine learning researchers and automatic scientific discovery researchers will think about the problem.
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