Random Puzzles 

Workings

Hint
Fill the 9-litre container first.

Answer
Here are the contents of the containers after each stage:

A = 9 litres, B = 4 litres
A     B
9     0     fill A
5     4     fill B from A (leaving 5 litres in A)
5     0     empty B
1     4     fill B from A (leaving 1 litre in A)
1     0     empty B
0     1     fill B from A
9     1     fill A
6     4     fill B from A (only 3 more litres fit in B)
6     0     empty B

This leaves 6 litres in container A.

Workings

Hint
The word LEMON appears 47 times.

Answer
The word LEMON appears 47 times.

Workings

Hint
The word starts with the letter Q.

Answer
Queue.

Less common words: aqueous, gooiest, obsequious, onomatopoeia, plateaued, plateauing, queued, queueing, queues, sequoia, sequoias, subaqueous.

All words: aqueous, archaeoastronomer, archaeoastronomers, archaeoastronomical, archaeoastronomies, archaeoastronomy, assegaaied, assegaaiing, banlieue, banlieues, beauish, blooie, camaieu, camaieux, cooee, cooeed, cooeeing, cooees, dequeue, dequeued, dequeues, enqueue, enqueued, enqueues, epigaeous, epopoeia, epopoeias, euoi, euois, euouae, euouaes, flooie, forhooie, forhooied, forhooieing, forhooies, giaour, giaours, gooier, gooiest, guaiac, guaiacol, guaiacols, guaiacs, guaiacum, guaiacums, guaiocum, guaiocums, hawaiians, homoiousian, homoiousians, hypoaeolian, hypogaeous, loaiasis, looie, looies, louie, louies, maieutic, maieutical, maieutics, meoued, meouing, metasequoia, metasequoias, miaou, miaoued, miaouing, miaous, mythopoeia, mythopoeias, nonaqueous, obloquious, obsequious, obsequiously, obsequiousness, obsequiousnesses, onomatopoeia, onomatopoeias, palaeoanthropic, palaeoanthropological, palaeoanthropologies, palaeoanthropologist, palaeoanthropologists, palaeoanthropology, palaeoecologic, palaeoecological, palaeoecologies, palaeoecologist, palaeoecologists, palaeoecology, palaeoenvironment, palaeoenvironmental, palaeoenvironments, palaeoethnologic, palaeoethnological, palaeoethnologies, palaeoethnologist, palaeoethnologists, palaeoethnology, palaeoichthyologic, palaeoichthyological, palaeoichthyologies, palaeoichthyologist, palaeoichthyologists, palaeoichthyology, pharmacopoeia, pharmacopoeial, pharmacopoeian, pharmacopoeias, plateaued, plateauing, prosopopoeia, prosopopoeial, prosopopoeias, queue, queued, queueing, queueings, queuer, queuers, queues, queuing, queuings, radioautograph, radioautographic, radioautographies, radioautographs, radioautography, radioiodine, radioiodines, reliquiae, rhythmopoeia, rhythmopoeias, saouari, saouaris, scarabaeoid, scarabaeoids, sequoia, sequoias, subaqueous, tenuious, terraqueous, toeier, toeiest, zoaea, zoeae, zooea, zooeae, zooeal, zooeas, zoogloeae, zoogloeoid, zooier, zooiest.

Workings

Hint
Does it start with January?

Answer
28.

The number of days in each month starting from October. The answer could also be 29 for a leap year.

The answer can't be 30, as the question specifically says that the answer is not 30, so it can't be the sequence starting with May.