![number magic trick number magic trick](https://i.ytimg.com/vi/GXaObRM1trk/maxresdefault.jpg)
First notice that not only the rows and columns add up to 55, but also the corners (13 + 6 + 21 + 15 =55), the 4 middle squares (7 + 12 + 14 + 22 = 55), the 4 squares formed by the 2 middle squares in the first and last row (16 + 20 + 10 + 9 = 55), and the 4 squares formed by the 2 middle squares in the first and last row (19 + 8 + 17 + 11 = 55). There are a couple of observations that are relevant. Which is a magic square with the desired magic constant: 55. In our case, since 21 = 4 × 5 + 1, we have that q = 5 and r = 1.
![number magic trick number magic trick](https://ecdn.teacherspayteachers.com/thumbitem/Magic-Number-Math-Trick-Beginning-of-the-Year-Activity-or-Ice-Breaker-054290700-1376066651-1500873414/original-818329-1.jpg)
Suppose someone asks you to produce a magic square with magic constant c > 34. This constant has to be bigger than 34, since we are not allowing repetition of numbers in the square and we have used the smaller numbers (from 1 to 16) to fill the square in the example above. There is a nice way of constructing a magic square whith arbitrary magic constant c. The sum of each row (or column, or diagonal) is called the magic constant of the magic square. A table that satisfies this property is called a magic square. Show that this is the case.Ĭall the table above A, and notice that each row, column and diagonal add up to 34, and each number appears exactly once. Subtract the reverse of the number you selected (the reverse of 321 is 123).Pick a three digit number so that the digits are decreasing (such as 321).No matter what your original number is, you get 2 at the end! Show that this is the case. Can you think of some modifications of your own?.Make sure you understand why the trick works in the odd case.Find someone and practice this trick together.Then the result of the process describe is: (1) 6a, (2) 3a, (3) 9a, (4) a. It is not hard at all! For instance, if the number selected was even, say x = 2a for some integer a. If you know a bit of algebra, you can show why the trick works. Then you tell me that the number I thought of is 2 × 2 + 1 = 5.
![number magic trick number magic trick](https://www.darksidedisplays.com/assets/images/29-59608_detail.jpg)
Then you ask me to divide it by 9, ignoring the remainder.You ask me to triple the number again.You ask me to add 1, and then divide by to.Otherwise the result of step 1 is odd, and then x = 2y + 1 Then if the result of step 1 is even, x = 2y. Suppose the final answer is y, and ask the person to tell you y.Then ask the person to divide the the result of step 3, ignoring the remainder.Ask the person to triple the result of step 2.If the resulting product is odd, ask the person to add 1 to it, and then divide by 2.If the resulting product is even, ask the person to divide it by 2.The resul of step 1 is either even or odd:.Lesson 6: Guessing a number and other tricksĪsk a person to think of an integer, say x.