Odd or Even; or, the Mysterious Addition.
You take a handful of coins, and invite another person to do the same, and to ascertain privately whether the number he has taken is odd or even. You request the company to observe that you have not asked him a single question, but that you are able, notwithstanding, to divine and counteract his most secret intentions, and that you will, in proof of this, yourself take a number of coins and add them to those he has taken, when, if his number was odd, the total shall be even; if his number was even, the total shall be odd. Requesting him to drop the coins he holds into a hat, held on high by one of the company, you drop in a certain number on your own account. He is now asked whether his number was odd or even; and, the coins being counted, the total number proves to be, as you stated, exactly the reverse. The experiment is tried again and again, with different numbers, but the result is the same.
The secret lies in the simple arithmetical fact, that if you add an odd number to an even number, the result will be odd; if you add an odd number to an odd number, the result will be even. You have only to take care, therefore, that the number you yourself add, whether large or small, shall always be odd.