## Monday, June 13, 2011

### The Wizard's Arithmetic

Once upon a time a knight went to consult a certain famous wizard.

"And art thou learned also in the magic of numbers?" asked the knight.
"Show me but one sample of thy wit in these matters."

The old wizard took five blocks bearing numbers, and placed them on a shelf, apparently at random, so that they stood in the order 41096, as shown in our illustration.
He then took in his hands an 8 and a 3, and held them together to form the number 83.

"Sir Knight, tell me," said the wizard, "canst thou multiply one number into the other in thy mind?"

"Nay, of a truth," the good knight replied.
"I should need to set out upon the task with pen and scrip."

"Yet mark ye how right easy a thing it is to a man learned in the lore of far Araby, who knoweth all the magic that is hid in the philosophy of numbers!"

The wizard simply placed the 3 next to the 4 on the shelf, and the 8 at the other end. It will be found that this gives the answer quite correctly—3410968.
Very curious, is it not? How many other two-figure multipliers can you find that will produce the same effect?
You may place just as many blocks as you like on the shelf, bearing any figures you choose.