The Last Two Oranges
An invented exercise, left in notebook form.
12 oranges. Five adults. Going home, not eating here.
No knife. One spare bag.
First division: two each. Ten allocated. Two surplus.
Keep this. It works.
I enjoy the clean division enough to linger over it. That is part of mathematics' attraction for me: a quantity becomes manageable without losing any of itself. Unfortunately, two oranges remain on the table while I admire the ten.
Preferences — ask, don't infer:
A and B: no extra fruit wanted.
C: wants one extra; dislikes carrying it loose.
D: has the spare bag; could use an orange tomorrow.
E: supplied the fruit; would like the surplus distributed.
Everyone already has somewhere to put the first two. The carrying problem concerns the surplus only. Otherwise I have designed an exercise in which nobody can get home and will spend the afternoon repairing my own premises.
H1: divide the surplus into five equal portions.
No knife. Also juice, peel, somewhere to eat. More equipment than the problem deserves.
H2: draw lots.
Why? Two people have said they don't want more. Equal chances of receiving an unwanted orange seems a peculiar triumph. Cross this out.
H3: D carries both surplus oranges to a shared turning, gives one to C, takes the other home for tomorrow.
Check the shared turning exists in the invented route.
Ask D. Do not appoint D.
This is the answer I like. It preserves the fair beginning and responds to a small obstacle. C needn't defend a dislike of loose fruit. D gets something useful too. Economics interests me here, where what people actually want changes the meaning of a satisfactory allocation.
Additional variable: D always carries things.
No. That has been inserted without evidence. Try: suppose D usually carries things. Is that a grievance? Unknown. D might enjoy being useful. D might be tired of everyone discovering the bag precisely when it is needed.
Possible next step: record previous occasions.
Better next step: ask whether carrying these two is welcome.
I can see the attraction of the record. Columns. Dates. An afternoon spent establishing a pattern, with no immediate need to risk an awkward answer. I could be meticulously fair to D on paper while leaving the actual oranges beside the actual hand that will pick them up.
Margin: the oranges are still invented. The delay is becoming quite recognisable.
Don't turn five people going home into a complete account of society. The first division was useful. The bag is useful. There needn't be a concealed injury for kindness to require a decision.
Put me in D's place, with the bag. I would like the orange for tomorrow. Carry C's as far as the turning.
Stop checking the route. In this exercise, I have already made it the same route.