32. IT DOESN’T ADD UP! 
The following two problems have more in common than meets the eye.
The first is a children’s rhyme:
As I was going to St Ives I met a man with seven wives. Every wife had seven sacks, Every sack had seven cats, Every cat had seven kits. Kits, cats, sacks and wives, How many were going to St Ives?
Too easy? Well, try this old favourite: Three men paid $30 to a bell-boy for a shared hotel room. The manager said this was too much, and sent $5 back. (Actually, I don’t believe this part of the story!) The bell-boy, at a loss to know how to split $5 three ways, pocketed $2 and gave $1 change to each man.
Now the room cost the men $27. The bell-boy received $2. What happened to the other $1 of the $30?
Solution
Each problem deliberately tries to lead the reader in the wrong direction.
In the first problem, only one person was going to St Ives, as we see from the first line. All the remaining information about the pedestrian traffic in the opposite direction contributes nothing to the solution!
The second problem is a little more tricky. Here, $2 and $27 are added together for no good reason, and the suggestion is then made that $1 is missing.
Suppose we do the accounting in the following way:
Actual cost of room (according to manager): $25
Money returned = $5
= $2 (pocketed by bell-boy) + $3 (given to men)
Now $25 + $5 = $30, and everything adds us correctly, so there is no problem.
As an analysis, we might say that each of these problems involves opposite directions. In the first, the characters are travelling in opposite directions, in the second the money is passing in opposite directions. Each problem is created by confusing these directions.
Extensions
Create your own problem of this type. Suitable situations might include payment of money and change, a person travelling north and south, a person travelling up and down in an elevator, or a merchant using weights and measures.
