- He spent all the time he should spend studying to play games
- He spent all the time he should spend studying playing games
Which one do you think is correct? Theoretically, (2),but is it not right for two "ing"s to appear in the adjacent positions?
- He spent all the time he should spend studying to play games
- He spent all the time he should spend studying playing games
Which one do you think is correct? Theoretically, (2),but is it not right for two "ing"s to appear in the adjacent positions?
(1) is definitely wrong.
There is no rule against using two words ending in -ing together, but if you don't like it for stylistic reasons, you could say
He spent all the time he should have spent in study in playing games.
Firstly, I'd use the past participle here:
He spent all the time he should have spent studying playing games.
As for the end of the sentence, either "to play" or "playing" would be correct, but they result in a very clunky sentence. It might be a little clearer if you reorder it:
All the time he should have spent studying, he spent playing games.