By Natalia Kokoromyti
Back in 2005 the German newspaper “Die Welt” (“The World”) decided to invite its readers to play an interesting and really promising game. It dared them to do the following: “Take a 3-digit number of your choice and write it down twice, hence forming a new integer. If for example your initial number was, let’s say, 761 your new number will be 761761. Now divide this 6-digit integer with 7 and the remainder of this division will be, from now on, your lucky number.” For someone that has somewhat of a close connection with the fundamentals of number theory it is quite intuitive that the possible remainders for when a number is divided by 7 are 0,1,2,3,4,5 and 6. So the newspaper invited its readers to write down on a postcard the lucky number that they got, and send it to the company’s headquarters in Berlin. Then the company would be obliged to send back to the reader a number of 100$ bills that is equal to their respective lucky number. If meanwhile, with your innate curiosity(!), you tried this out yourself I bet that the lucky number that you got is 0! Am I mentalist? Maybe, conceivably, possibly. Yet I have to admit that this observation should not be attributed to my mind-reading abilities that I frequently attempt to finesse, but to an even more brain-fuddling property of the integers. Because let me tell me you, you weren’t the only one whose lucky number was 0. Actually all the readers that took part in this problem got 0 as their lucky number! The explanation of this phenomenon lies in a hidden property of the integers. To be more specific, notice that writing a 3 digits number two times consecutively is equivalent to multiplying this 3-digit number with 1001. And because 1001 is a multiple of 7, so is the 6-digit number. Note that with the same reasoning we can use other divisors of 1001, like 11 or 13 instead of 7.
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2/11/2024 08:44:12 am
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