Suppose you get a short input of increasing integers, say, "2 4", can you figure out what integers come after 4? If you assume the second integer is +2 greater than the first, then the next integer should be 6; but if you assume the second integer is double the first integer, then perhaps the next integer is 8. However, if the short input was "2 4 8", then you can almost be sure that the next integer is 16.
For instance, if the program receives the following input:
The program may assume that the next integer is the previous integer plus 10, thus it will generate:
24 34 44 54 64 74 84 94 104 114
but if the program receives the following input instead:
4 14 34
then it may hypothesize that the next integer is the previous multiplied by 2 plus 6.
74 154 3314 634 1274 2554 5114 10234 20474 40954
This is an open-ended problem that we're presenting, in other words, the input list of integers may have very interesting properties (e.g. a fibonacci sequence), there is no particular set of integer sequences that we are testing. So, be creative! try to identify as many sequences as you can think of.