The researchers found that after people spent at least 15 sec in sleep onset, their chances of figuring out the hidden trick to solving the math problem tripled.

Sleep onset / stage 1 sleep is a stage when you're drifting into slumber, when we're not quite asleep but also not quite awake.

This was not seen in subjects who didn't wake up and continued on to deeper sleep stages.

This led the researchers to suspect that the brain activity during stage 1 sleep likely ignites creative sparks"; that achieving it requires a balance in falling asleep easily against falling asleep too deeply," - authors