Solution - Magical Math Trick Quiz

Thanks to everyone who participated in the subject quiz presented in the last post – the quiz certainly was not multiple choice.

 

There were two responses that explained how the math trick worked – both our SC businessman & new subscriber JC presented the correct principles for solving the problem – I posted their responses in the comments section of Magical Math Trick Quiz. 

 

Most people said things like "HOW CAN THIS HAPPEN? . . . I FEEL SPOOKED!!" after realizing that any number selected resulted in #9 – BO's Farewell Speech.

 

My solution to the quiz is as follows:

 

First convert the wording instructions to an algebraic expression – this starts with (3x+3)(3) & simplifies into 9(x+1) where x = integers from 1 to 9.

 

Substituting "1" for "x" produces 18 from the expression; "2" produces 27; "3" produces 36, & the pattern becomes obvious that whatever number from 1 to 9 selected results in the addition of the digits equaling "9".

 

This phenomenon occurs because as the number selected increases the tens digit goes up while the units digit goes down by the same number meaning that the sum of the digits remains constant – in our case 9.  For example for x = 5 the expression = 54; increase x to 6 & the expression = 63.  When the tens digit went from 5 to 6 the units digit went from 4 to 3.

 

This phenomenon occurs for other strings of numbers as well.  Substitute integers from 11 through 19 & add the three digits of the resulting number from the algebraic expression & you will also get "9".  For x = 11 the expression = 108; for x = 15 the expression = 144.  In every case from 11 to 19 the sum of the three digits = 9.

 

Carry it out for 111 through 119.  For x = 111 the expression = 1008; for x = 115 the expression = 1,044.  In every case from 111 to 119 the sum of the four digits = 9.

 

The key is all of the units digits are integers from 1 to 9 (same as the original math trick) & the tens & hundreds digits are all the number "1".