Skilful conjuring, viewed close up, can be very perplexing, and it becomes astonishing if the conjuror shows you how it was done. How easily he misled you, how blind you were to what was going on right under your nose, how simple it was.
You soon realize how incompetent a judge you would be in the face of claims of spoon bending or levitation. Scientists are the easiest to fool, they are not used to Nature conspiring to trick them. They believe almost everything they see is true. Magicians believe nothing.
In this spirit, I want to relate to you a little mathematical story, adapted from a version by Frank Morgan, that is an example of verbal conjuring. You keep track of everything in the story but something seems to disappear in the telling : “a sum of money no less” and you have to figure out where it went, or indeed, whether it was ever there.
There are 3 travelers arrive at a cheap hotel late at night, each with just $10 in his wallet. They decide to share one large room and the hotel charges them $30 for a one night stay, so they each put in $10. After they have gone up to their room with the bell boy carrying their bags, the hotel receptionist receives an email from the head office of the hotel chain saying that they are running a special offer and the room rate is reduced to $25 for guests staying tonight. The receptionist, being scrupulously honest about such things, immediately sends her bell boy back to the room of the 3 new guests with a $5 note for their rebate. The bell boy is less scrupulous. He had not received a tip for carrying their bags and he can’t see how to split $5 into 3, so he decides to keep $2 for himself as a “tip” and give the 3 guests a rebate of $1 each. Each of the 3 guests has therefore spent $9 on the room and the bell boy has $2 in his pocket. That makes a total of $29. But they paid $30 – what happened to the other $1 ?