Online Math Center

How To Develop Critical Thinking with Numeric Puzzles

Applying the universal rule of “simple things always look complicated”, we can admit the fact that old math games can give us a headache even today with all the technical help. Numeric puzzles can be the trickiest math games, but they are amazing tools to develop critical thinking in children. 

What Are Numeric Puzzles?

Numeric puzzles are sets of numbers with one or multiple missing digits. Usually, they have a solving key that has to be applied in order to solve the puzzle. Numeric puzzles often come with a rule, since solving them could have infinite possibilities. 

Types Of Numeric Puzzles



One of the most popular numeric puzzles, Sudoku’s particularity is filling a 9 x 9 grid with digits so that on each column, and on each row, the nine 3 x 3 sub grids contain all numbers from 1 to 9.  


There are 4 rules of Sudoku:


  1. Each row contains numbers from 1 to 9, without repetitions. 
  2. Each column contains numbers from 1 to 9, without repetitions. 
  3. The number can only occur once per block.
  4. The sum of every single row, column, and block must be 45.


Try out some online Sudoku, and you will see how your brain trains to perceive logical situations faster! 




This is a numeric puzzle with an easier solution than Sudoku because the sum of numbers you have to obtain is mentioned at the end of each row, and column. Therefore, you have to find numbers that result in the digit stated vertically and horizontally, just like in the example below: 


Yohaku also has a restrictive rule, such as “Use prime numbers”, so you have the use only prime numbers in order to solve the puzzle


Magic Geometry


Numeric puzzles are made of equal rows and columns, in a square or triangle shape. Each line of the geometrical shape (horizontal, vertical, and diagonal) add up to the same sum, and each box has to contain a different number. In a  3×3 square, each line can add up to 15, for example. In a  4×4 magic square, each line could equal 34. In a triangle, the three lines could add up to 10, or any number. 


Math riddles


Some students have a more developed visual memory, others concentrate better without a paper. For students that like to think about things,  math riddles are the best way to train critical thinking. 


Some common, and fun math riddles are: 

  • How do you make the number 7 even without addition, subtraction, multiplication, or division?   


  • Can you write down eight eights so that they add up to one thousand?


  • How can you take 2 from 5 and leave 4?


  • Lily is a lilypad in a small pond. Lilly doubles her size each day, On the 20th day, she covers the whole pond. On what day was Lily half the size of the pond?


  • The head of a whale is six feet long; his tail is as long as his head and half his body, and his body is half of his whole length. How long is the whale?

Do you know the answers to these math riddles? 


How to solve numeric puzzles? 


As it has been mentioned before, each numeric puzzle has a solving key; even the restrictive rule in the case of Yohaku puzzles can guide the player to solve the math puzzle. 


There are two general approaches to solving any numeric puzzle. 


  1. Determine a commonality between numbers, or sets of numbers. There has to be a pattern.


  1. Numeric puzzles usually work with addition and subtraction, multiplication, and division. These are the 4 math operations that have built up math games since ancient times. 

Why should you solve numeric puzzles?


“Oldies, but goldies”, math exercises from distant times were using the person’s ability to identify logical patterns and apply them. People had to act as computers which encouraged them to be more critical and fast at technical operations. Nowadays, technology facilitates problem-solving, so our brains become lazy. By solving numeric puzzles, children and adults will notice considerable progress in: 


  • Focusing on tasks at hand; 
  • Identifying patterns quickly; 
  • Applying logical reasoning to discussions;
  • Improving mental calculations;
  • Enhancing strategic thinking;
  • Developing planning skills;
  • Encouraging problem-solving capacity;
  • Developing hand-to-eye coordination;
  •  Reducing degenerative mental diseases; 


Students have less and less patience due to instant, and automated technological devices. Lack of concentration and boredom at school can indicate that the student’s mental capacity is not stimulated in a healthy way. However, games including numeric puzzles can help improve concentration and offer a fun way of learning. 


At the Online Math Center…


We focus on teaching mathematics that applies in daily life. Our math tutors offer programs for middle school students, but also to students that want to individually prepare for math competitions. We are dedicated to providing students with a learning environment that includes useful tips and extra-curricular activities that improve development. 

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