Arithmetic Magic Matrix

Select exactly one square in every row and in every column and check that the sum (or the product) of numbers in the selected squares does not depend on your selections. Can you explain why? How are these tables constructed? Try small sizes, 2×2, 3×3, etc.

Two Numbers Guessing Game

As you might have noticed, the two numbers of which you are asked to select one, always have different parities: one is always even, the other is always odd. You are also asked to multiply one of them by an even number, the other by an odd number. It's always the case that one of the products is even. The other may be either even or odd. In the former case, the sum of two products is even, in the latter case it's odd. Checking the parity of the sum, I can immediately tell which number you selected.

Barcode Magic

The ubiquitous barcodes serve as the basis for the following computer magic. The applet below is made to represent the standard barcode representation of the UPC-A codse . This is something that is commonly (and not quite correctly) referred to as the barcode. Do the following: pick up a product. It could be a bottle of Cola, an ice cream pack, or anything else with an UPC-A code and a barcode on it. Initially the applet displays 12 question marks. By clicking on them you can upgrade each to any decimal digit. Do this with 11 digits and leave one question mark. Press the "Check" button. The computer will announce the missing digit.

Magic in a Square

N² numbers are arranged in a square pattern. Select one of the numbers and try answering computer queries. After two attempts, computer will reveal your selected number.

An Arithmetic Magic Trick

Think of a 2-digit integer. Subtract from the number the sum of its digits and find the result in the table below. Note that each cell of the table contains a number and a geometric shape. Concentrate hard on the shape that shares a cell with the result of your calculations. When ready, press the "Check it!" button ...