Random Puzzles 

Workings

Hint
Look at the first letter of each month.

Answer
199.

Take the first letter of the month, and find its position in the alphabet: S = 19.

Then take the number of letters in the month: September = 9.
January    10 7
February   6 8
March      13 5
April      1 5
May        13 3
June       10 4
July       10 4
August     1 6
September  19 9

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
How many pieces on the top layer had two sides with icing?

Answer
15 pieces.

Reasoning
On each layer there are 4 pieces with exactly two sides of icing.

Therefore Kevin ate 12 pieces, leaving 15 for the guests.

Workings

Answer
There is no fool like an old fool.