Oddly Wired
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sleep

Sleeping on it improves your problem-solving abilities.

A 2004 study found that participants who slept were significantly more likely to gain insight into a hidden mathematical rule than those who remained awake.

Participants who slept were approximately twice as likely to gain insight compared to those who stayed awake, rather than the sleep-deprived being specifically '50% less likely'.

The solution you need is likely already in your head, waiting for sleep.

Where this comes from

Study
Wagner et al., 2004, Nature
What the check found
Wagner et al. (2004) demonstrates that sleep promotes insight, not merely puzzle-solving. The '50%' figure is a rough summary that does not accurately reflect the study's reported improvement rates.
Confidence
Solid, with limits

Related

One of these every day, and every one names the study it came from. When a finding is contested, it says so.