Mathematical Trickery

4 3 2 5 7 6 The student needs to choose one number in the matrix and circle it. Then you cross out all the other numbers in that row and column and the student chooses another number and you make similar crossings out etc. until all the numbers in the matrix have been either circled or crossed out. Then the student needs to add up the circled numbers (could get other students to help out) and hopefully he/she will spot that this is a significant number (although experience shows that sometimes a bit of hinting may be necessary!). Run through with at least two students – then show how it works. (In this case 21 is the significant number.)

11 13 8 31 14 16 34 15 17 12 35 18 20 38 92

3 2 1 1 2 4 4 3 2 5 7 6 We add in these extra green numbers. Note that each number in the grid is a sum of the green number which is at the top of the column it is in and the green number at the start of the row which it is in. All the green numbers together add up to our secret number 21

5 7 2 25 6 9 10 13 11 13 8 31 14 16 34 15 17 12 35 18 20 38 92

29 = 3 + 1 + 8 + 7 + 4 + 6 3 1 8 7 4 6 10 8 15 7 5 12 9 14 Try a simple 3X3 grid. If our secret number is 29, then we need to find six numbers which add up to 29. Write these round the edge of the grid. Fill in the grid by adding up the green numbers in the rows and columns. Then your magic matrix consists of the black numbers in the grid.

a + b + c + d + e + f = special number a b c d e f a+d b+d c+d a+e b+e c+e a+f b+f c+f