- John said to Fred, "If I can guess the number you are left with will you give me the amount in money?"
- "Yes," said Fred. "I'm not averse to this. So long as I can ask you."
- So John said to Fred, "Think of a number and don't tell me."
- So he did and he didn't.
- "Add three," said John. "Multiply by two. Subtract by four. Alright?"
- "Yes. Got it."
- "Divide by two and subtract the original number."
- "Right," said Fred.
- "So you owe me one pound," said John. "Because you have been left with a one."
- "Very good indeed," said Fred. "So the deal is I can now ask you."
- "Yes," said John, "So pay up."
- He did, and said, "So you think of a number."
- "Yes."
- "Now add to it the next number up; that is, one greatest."
- "Got it."
- "Add nine. Then divide what you have got by two. In other words, halve it."
- "Half the value it is."
- "And then subtract from that the number you started with."
- "I have."
- "Give me five pounds."
- "Fantastic. I am much the poorer."
- "Yes," said Fred, "In algebra it is called an identity, because it is not even an equation. No matter what is the starting point, it always comes back to the figure I selected and not the one you select. In other words x is altered but y stays the same. In an equation the attempt is to find out how another variable y is affected by the number chosen x.
- "It's quite a mute point. Which means you could guess the number I start with?"
- "Yes, if you tell me the final answer; anyone can adopt the basic approach to also identify the first number.
- So it is like the card trick, like the one broadcasted the other day on the magic show.
- So think of a number."
- "Right," said John.
- "Double it. Add four."
- "With you."
- "Now divide that by two and then add thirteen."
- "So now you need to ask me what I have got left."
- "What have you got left?"
- "Twenty one."
- "You started with six. You owe me six pounds."
- "Hang on a minute; this was not for money."
- "Yes but the rules are pretty much the same. In this case they were achieved by doing two x plus four in brackets then divided by two and adding thirteen."