General confusion:
* Bewilderment
* Confusion
* Disorientation
* Perplexity
* Uncertainty
* Mystification
More specific to intellectual puzzles:
* Bafflement
* Consternation
* Quandary
More informal:
* Scratching your head
* Being stumped
* Not getting it
The best synonym for "puzzlement" will depend on the specific situation and the tone you want to convey.