Hello, there is the same trick in french about the '9' property but also, once the person chooses a number from 1 to 9, then the performer asks multiply that number by 3 and by 3 again, which will always make a multiple of 9 : Then the neat trick. The person is asked to remove 5 from the sum of digits of the number which will invariably will give 4 : Then : from that number, choose the letter from the alphabet whose digit is 4 : will lead to D. From that letter : choose a country beginning by that letter : The thing is : only Denmark begins with a D , 99 % of people will choose Denmark. Now from that country choose a fruit with the last letter of the name of that country : Invariably people will chose KIWI since this is the first thing a person will think if asked, there are other fruits like kumquat but by the simple choice principle the person will choose kiwi. Then the punch line : you say there are no kiwis in Denmark.... Surprise! That trick works most of the time. There is another one based on that 'simple choice principle' If you ask a person : without hesitation, think fast : choose a TOOL and a COLOR: most people will answer hammer and red. (marteau et rouge in french). That one works about 4/5 of the time. These are classics, I use them in classes to keep their attention ... Best regards, Simon Plouffe Le 2016-10-07 à 21:53, James Propp a écrit :

Art Benjamin recently gave a talk in which he performed the following trick: An audience member secretly picks a positive integer N whose digits are distinct and increasing. The audience member uses a calculator to compute 9N. The magician is able to divine the sum of the digits of 9N without knowing N. That's because that sum is always 9.

Art tells me he learned this fact from an article in Mathematics Magazine (Vol 87, No 3, June 2014) called "Surprises, Surprises, Surprises", written by Felix Lazebnik. Lazebnik's statement is slightly more general: "Consider any positive integer N whose (decimal) digits read from left to right are in non-decreasing order, but the last two digits (tens and ones) are in increasing order. Prove that the sum of digits of 9N is always exactly 9."

Lazebnik says that he heard about the problem from applied mathematician named Valery Kanevsky, who tells me he does not know the problem's provenance.

Do any of you know anything about this?

Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun .