MATHEMATICS PUZZLES

 

INTRODUCTION

Puzzle is any problem that challenges the mind, stimulates thinking for potential solutions and provides a rewarding experience upon solving it. Many games—such as solitaire, chess, and checkers—include numerous puzzles. Other common game-puzzles include crossword puzzles, which appear daily in nearly every newspaper around the world, jigsaw puzzles, and the mechanical puzzle Rubik's Cube.

Puzzles can be grouped into three broad classes: riddles and word puzzles, mathematical and logic puzzles, and physical and mechanical puzzles. 

Some of the first number puzzles were included in an important ancient Egyptian mathematical document composed about 1650 BC and known as the Rhind Papyrus. Magic squares, another early form of number puzzle, originated in China before the end of the 1st century. A magic square puzzle forms a square array of numbers so that the rows, columns, and major diagonals all have equal sums.

Geometric puzzles were studied by Greek mathematician Archimedes in the 3rd century BC. The Loculus of Archimedes is a dissection puzzle in which a square is cut into 14 pieces that are to be reassembled (a type of put-together puzzle) to form silhouettes of people, animals, or objects. In 1902 Dudeney published another type of geometric puzzle: Cut an equilateral (equal-sided) triangle into four pieces that can be reassembled into a square. 

Logic puzzles are puzzles that require deductive reasoning with little or no numerical calculation. 

OBJECTIVES OF MATHEMATICS PUZZLE

Motivation to Learn

Because many students enjoy working on these puzzles, they can be easily motivated to adopt learning strategies that will improve their puzzle-solving skills. Grid number puzzles provide strong intrinsic motivation to solve for unknown numbers from a handful of clues. As many math problems have a similar form, students who enjoy solving these puzzles can develop positive attitudes toward other forms of math in non-puzzle contexts as well. I have taught puzzle math to students in grades three to six. In these classes, I have found that students show a significant positive change in their attitudes toward math after a year of recreational math activities. Professor Harold Reiter of University of North Carolina, along with Professor Novak of Ithaca, also found that teaching puzzle math has a positive influence on student attitudes towards math.

Educational Value of Puzzles

Even without supervision, students can learn to be creative and persistent after working on many hard grid puzzles. In my classes, I augment self-exploration of grid puzzles with a guided exploration that teaches problem-solving, reflective learning and algebra techniques.

PUZZLE SET (WITH ANSWERS)

1.

What number should replace the question mark?

2.	What number should replace the question mark?

3.

What number should replace the question mark?

4. Can you find four consecutive prime numbers that add up to 220?

5. Take 9 from 6, 10 from 9, 50 from 40 and leave 6.
How Come??

6. What do you get if you add 3 to 300 five times?

7. Find three positive whole numbers that have the same answer added together or when multiplied together.

8. When deepak was six years old he hammered a nail into his favorite tree to mark his height. Five years later at age eleven , deepak returned to see how much higher the nail was. If the tree grew by ten inches each year, how much higher would the nail be?

9. In a new Engineering Hostels containing 100 rooms. Ankit Garg was hired to paint the numbers 1 to 100 on the doors.
How many times will Ankit have to paint the number eight ?

10. 5+3+2 = 151022
9+2+4 = 183652
8+6+3 = 482466
5+4+5 = 202541
THEN ;
7+2+5 = ?

ANSWERS

Question No.	Answer	Solution
1	0	Looking at lines of numbers from the top : 9×8 = 72; 72×8 = 576; 576×8 = 4608
2	17	It is the sum of the two digits(9 + 8) in the quadrant opposite
3	55	Each number indicates its position in the grid. 55 indicates row 5 columns 5
4	220	47 + 53 + 59 + 61 = 220
5		SIX - 9 (IX) = S 9 (IX) - 10 (X) = I 40 (XL) - 50 (L) = X => SIX
6		303, 303, 303 , 303 , 303
7	1,2, & 3	1 x 2 x 3 = 6 and 1 + 2 + 3 = 6
8		The nail would be at the same height since trees grow at their tops
9	20 times	8,18,28,38,48,58,68,78,98,80,81,82,83,84,85,86,87,88,88(2),89
10		143547