Fun with Mathematics- Mathematical Toys , Games and Magic

I am starting a new series of posts this year on making Mathematical toys, puzzles and games which one can create at home using just paper / stiff card, a bit of drawing ,painting ,cutting and gluing skills. You will also learn how you can be a " Mathemagician" and impress your friends with magic ( using playing cards, dice, ropes...etc)  based on simple mathematical principles and not on your sleigh of hand !

This series hopes to awaken your creative and critical thinking skills and use not only your brains but your hands as well

So here we go on our very first "Mathemagical roller-coaster ride of fun and learning "....  

How would like to show off your mathematical prowess to your friends ? Just take a print out of diagrams shown in Fig-1 and Fig-2 on thick paper , cut along the outline , fold along the vertical lines and glue the sides using the tabs marked ... "*" . You now have 4 rectangular sticks of different colours with single digit numbers.

Ask your friends to arrange these 4 sticks next to each other so that they  get "four 4 digit numbers" ( See Fig-3 for examples of two such arrangements)

Now you tell them that you can instantly declare the total of these "four 4 digit numbers" . Your friends  will need time or may even need to use  the calculator to total these numbers ,  but you can immediately reveal the total ....and leave your friends baffled.

 

How do you do this ? Simple ... read on....and here is the secret behind the trick....

The total will always be a five digit number starting with 2. For any given combination of numbers just look at the third horizontal line of numbers .... it's 2965 in Arrangement -1 ( Ref Fig -3) . All you have to do is minus 2 from the last digit to get 2963 . These are the remaining four numbers of the total .....22963.  Similarly for the Arrangement -2 the total is 27255!

You can change the 4 sticks to any combination , but the formula for the answer will always be in the third horizontal line /row

Can you discover the logic behind the trick? Using your discovery can you now make your own set of rectangular sticks with appropriate numbers meeting the above formula?

Leave your answer / logic as a comment or write to me . My e-mail is  xploreandxpress@gmail.com