When “甘” fills a head
Why it is in the set
Partly for cake. Mostly for the second meaning. A head full of 甘 can be a head that wants something sweet, or a head that is currently negotiating with itself about what it deserves, and the ambiguity is doing real work in a joke generator. The English quips lean on the first meaning, because the second does not survive the crossing without a paragraph of explanation.
What a head full of it looks like
The reward you have already decided on before the task is done. Knowing exactly what is in the cupboard. The small negotiation, conducted entirely in your own head, in which you win.
Words that use it
甘い (amai, sweet, or lenient), 甘味 (amami, sweetness), 甘酒 (amazake, a sweet drink made from rice), 甘やかす (amayakasu, to spoil someone), 甘く見る (amaku miru, to underestimate).
Kanji it turns up with
食 (food) and 茶 (tea) are its natural company. 甘 on top with 疲 or 忙 (busy) behind it usually reads as someone owed a break rather than someone owed a cake.
Where “甘” comes from
A mouth, 口, with a line drawn inside it. The line marks the thing being held on the tongue. It is one of the small number of kanji that point at a spot rather than draw an object.
The second meaning is the interesting one. 甘い said of a person means lenient, indulgent, too easy on them. 甘える (amaeru) is a verb with no neat English equivalent: to presume on someone's affection, to let yourself be looked after.
So the same character covers dessert and the reason you did not do the washing up.
A line you might get for “甘”
“Something sweet is owed. The terms were set this morning.”
Count the “甘” in your own headOthers in “Appetites”
“甘” is filed under “Appetites”. These are the rest of that group.
The 36 kanji
This is entirely a joke and has nothing to do with any real person.