brainteaser

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brainteaser [noun]

A problem for which it is hard to find the answer, especially one which people enjoy trying to solve as a game

US /ˈbreɪnˌtiː.zɚ/ 
UK /ˈbreɪnˌtiː.zər/ 
Example: 

The paper publishes two brainteasers every Saturday.

Longman Dictionary of Contemporary English

brain teaser

ˈbrain ˌteaser BrE AmE noun [countable]
a difficult problem that is fun trying to solve
 

Oxford Advanced Learner's Dictionary

brain-teaser

ˈbrain-teaser [brain-teaser brain-teasers]       noun
a problem that is difficult but fun to solve

There were some real brain-teasers in the quiz.

Cambridge Advanced Learner's Dictionary

Cambridge Advanced Learner's Dictionary - 4th Edition
 

brainteaser / ˈbreɪnˌtiː.zə r /   / -zɚ / noun [ C ] ( also teaser )

a problem for which it is hard to find the answer, especially one which people enjoy trying to solve as a game:

The paper publishes two brainteasers every Saturday.

© Cambridge University Press 2013

Collins Advanced Learner’s English Dictionary

brain teaser

also brain-teaser
(brain teasers)

A brain teaser is a question, problem, or puzzle that is difficult to answer or solve, but is not serious or important.

= puzzle

N-COUNT

Merriam-Webster's Advanced Learner's Dictionary

brainteaser

brain·teas·er /ˈbreɪnˌtiːzɚ/ noun, pl -ers [count] : a puzzle that is difficult to figure out or solve