The Maths-Classics project

Assignment 10

A Roman numbers game

The following number game was known to the Romans. As they had no algebra they found the results of the game amazing and probably believed the person, who was telling them what to do, possessed magical powers!!

 

Firstly work through the game with a friend and record your results.

Secondly try to write down, using our algebraic notation, the result of each step. You may need to distinguish between an odd starting number and an even starting number - ask your Maths teacher to help you write down any odd or even number if you find this difficult.

 

THE GAME

1. Ask someone to think of a number [maybe write it down in a secret place!]

2. Tell them to treble it

3. Ask them to divide the new number into two equal shares, or two shares that differ by 1.

4. Get them to treble the larger share.

5. Ask them to divide this by 9, and take the whole number part of the answer (ignore the remainder).

6. Tell them to multiply this by 2 ( but add 1 if there was a remainder in step 5 )

7. Announce that this was the number they were thinking of! Look at the amazement on their face!