Is a score of 242 possible in a game of ten pin bowling?

Yes. The maximum score in tenpin Bowling is 300. One way to bowl a 242: 1st frame - strike

2nd frame - strike

3rd frame - seven on the first ball and a spare on the second ball

4th frame - strike

5th frame - strike

6th frame - seven on the first ball and a spare on the second ball

7th frame - strike

8th frame - strike

9th frame - strike

10th frame - strike on the first ball, eight on the second ball, spare on the third ball

X----X----7/----X----X----7/-----X-----X-----X-----X8/ 27...47...67....94..114..134...164..194..222...242