37. GETTING FIRED UP 
Nick, Darryl and Ian live together in an old house which is heated by an open fire. In winter, the lads are always scrounging firewood to keep warm.
One cold night, Nick came home with three logs for the fire. and Darryl brought in five logs. Ian rushed in late with no logs.
‘Here is 80 cents as my contribution,’ he said. ‘Share it between you.’
‘I think we should have 40 cents each,’ said Nick. ‘After all, we are all getting the same warmth from the fire.’
‘Not so,’ answered Darryl. ‘Since I brought in five logs, I should get 50 cents.’
After a long and heated(!) debate, Nick finished up with 10 cents, and Darryl with 70 cents. Can you explain why this is a fair and equitable division?
Solution
If we assume that Ian’s contribution of 80 cents represents a third of the value of the logs then the total value of the logs is three times this, that is, $2.40.
Since there are eight logs, each log is worth 30 cents. Thus Nick has contributed three logs of total value 90 cents, and Darryl has brought five logs of value $1.50.
On the other hand, each has received an equal share of the fire. Neglecting the odd match and kindling, we can say that the fire was worth the value of the logs, that is, $2.40. Since this was shared equally, each of the lads received 80 cents worth of heat.
So finally,
Nick received 90– 80 = 10 cents;
Darryl received $1.50 – 80 cents = 70 cents;
Ian paid his 80 cents for his share of the fire.
Pretty intelligent lads, I reckon!
Extensions
If Nick and Darryl had each brought in four logs, we would expect that they would have shared the 80 cents equally between them.
Does applying the above argument give this conclusion?
