puzzleyoudaoicibaDictYouDict[puzzle 词源字典]
puzzle: [16] The origin of puzzle is, appropriately, a puzzle. One suggestion is that it may be derived from the now obsolete verb pose ‘interrogate, perplex’ (which survives in poser ‘difficult question or problem’), a shortened form of appose ‘interrogate or question severely’. This came from Old French aposer, a variant of oposer, from which English gets oppose. Another possibility is some connection with the Old English verb puslian ‘pick out the best bits’, which is reminiscent of puzzle out ‘find or solve by laborious reasoning’ (although that sense of puzzle is not recorded until the end of the 18th century).
[puzzle etymology, puzzle origin, 英语词源]
problem (n.)youdaoicibaDictYouDict
late 14c., "a difficult question proposed for solution," from Old French problème (14c.) and directly from Latin problema, from Greek problema "a task, that which is proposed, a question;" also "anything projecting, headland, promontory; fence, barrier;" also "a problem in geometry," literally "thing put forward," from proballein "propose," from pro "forward" (see pro-) + ballein "to throw" (see ballistics).

Meaning "a difficulty" is mid-15c. Mathematical sense is from 1560s in English. Problem child first recorded 1920. Phrase _______ problem in reference to a persistent and seemingly insoluble difficulty is attested at least from 1882, in Jewish problem. Response no problem "that is acceptable; that can be done without difficulty" is recorded from 1968.