If Orwell wrote "Animal Farm" about schools, the dogs would be schoolyard bullies, True.
I managed to find the complete exercise on the Internet, given that you haven't provided us with all options given to you.
1. cogitating = contemplating
To cogitate means to think about something (cogito in Latin literally means 'to think). Contemplating means to mull over a couple (or a lot) of options which is what Mr. Gamefield is doing in the excerpt above - he is thinking of ways to pay his rent.
2. cudgeling = beating
A cudgel is a short stick which you can use as a weapon. So if you cudgel something or someone, it means that you are beating them with a cudgel, because it is a thick stick, almost like a bat. So this person was metaphorically cudgeling his brain, but literally cudgeling his donkey.
3. regaled = rewarded
The verb to regale has two meanings - it can either mean 'to entertain someone,' or it can mean 'to supply someone with something.' Here, the latter meaning is used - the donkey thought he would be given a cabbage-stalk or two for his hard work.
Answer:
A. Writing to a former teacher to request a reference for a new job
Explanation:
