Number Puzzles and Games Worksheet is available here. This worksheet makes you familiar with the concept and different types of games and puzzles. Practice various questions to get knowledge of puzzles. Solve questions of number puzzles and games provided with solutions here and understand the approach used to solve various questions.

**Question 1.**

Complete the following magic square?

**Solution:**

Add the numbers in the column which is completely filled with numbers.

Calculate the magic constant

magic constant = [n (n² + 1)] / 2

Sum = [4(4² + 1)] / 2

= [4 (16 + 1)] / 2

= [4 * 17] / 2

= 68 / 2 = 34

The sum of all rows, columns, and diagonals is 34.

Sum up the numbers in the column which is completely filled with numbers. Proceed with completing the row or column which has three numbers and only one cell empty.

3 | 14 | 13 | 0 |
---|---|---|---|

8 | 5 | 6 | 11 |

4 | 9 | 10 | 7 |

15 | 2 | 1 | 12 |

Sum = 3 + 14 + 13 + 0 + 8 + 5 + 6 + 11 + 4 + 9 + 10 + 7 + 15 + 2 + 1 + 12 = 120

**Question 2.**

In the 4 x 4 magic triangle, fill in the numbers from 0 to 8 (without repetition) in the nine circles so that the numbers on each side of the triangle add up to 13.

**Solution:**

The simple thing is place 0, 1, 2 at the vertices of the triangle. and remaining on other unfilled fields.

**Question 3.**

In the magic box, there are 10 hidden mines. Around the numbered square the total number of mines hidden in the 8 squares, indicates the numbers in various squares. Now you have to find 10 mines.

2 | 0 | 1 | |||||
---|---|---|---|---|---|---|---|

3 | 1 | 2 | |||||

1 | 0 | 1 | |||||

2 | 1 | 0 | |||||

1 | 0 | 1 | |||||

1 | 1 | 1 | 1 | ||||

1 | 1 | 2 | 2 | ||||

1 | 1 | 2 |

**Solution:**

First of all cross out all empty cells around the square 0.

2 | x | 0 | x | 1 | |||
---|---|---|---|---|---|---|---|

3 | x | 1 | x | 2 | |||

1 | 0 | x | 1 | x | |||

2 | x | x | 1 | 0 | |||

1 | x | 0 | x | 1 | x | ||

1 | 1 | 1 | x | 1 | |||

1 | 1 | 2 | 2 | ||||

1 | 1 | 2 |

The hint is Mine is available at the lower-left corner of the grid.

Based on this hint and data provided on the question, 8 mines are represented using the M letter in the cells.

M | 2 | M | x | 0 | x | 1 | x |
---|---|---|---|---|---|---|---|

x | 3 | x | 1 | x | 2 | M | x |

M | 1 | 0 | x | 1 | M | x | x |

x | 2 | x | x | x | x | 1 | 0 |

M | 1 | x | x | 0 | x | 1 | x |

1 | 1 | x | 1 | x | x | 1 | x |

x | 1 | x | x | 1 | 1 | 2 | 2 |

M | x | 1 | x | 1 | x | M | x |

**Question 4.**

Find the values A, B, C, D, and E to complete the number triangle given below:

**Solution:**

We can say that each number is equal to the product of two nearest numbers in the row just above it.

So, A = 2 * 4 = 8

B = 8 * 2 = 16

C = 2 * 16 = 32

D = 16 * 64 = 1024

E = 64 * B = 64 * 16 = 1024

**Question 5.**

Solve the sudoku provided below.

1 | 4 | 8 | 9 | 6 | ||||
---|---|---|---|---|---|---|---|---|

7 | 3 | 4 | ||||||

1 | 2 | 9 | 5 | |||||

7 | 1 | 2 | 6 | |||||

5 | 7 | 3 | 8 | |||||

6 | 9 | 5 | 7 | |||||

9 | 1 | 4 | 6 | |||||

2 | 3 | 7 | ||||||

8 | 5 | 1 | 2 | 4 |

**Solution:**

The simple trick is to take one row or column which are having more filled numbers and less unfilled numbers.

In this question, the column which is having less unfilled cells is the first column. Continue the process to get the solution easily.

1 | 5 | 2 | 4 | 8 | 9 | 3 | 7 | 6 |
---|---|---|---|---|---|---|---|---|

7 | 3 | 9 | 2 | 5 | 6 | 8 | 4 | 1 |

4 | 6 | 8 | 3 | 7 | 1 | 2 | 9 | 5 |

3 | 8 | 7 | 1 | 2 | 4 | 6 | 5 | 9 |

5 | 9 | 1 | 7 | 6 | 3 | 4 | 2 | 8 |

2 | 4 | 6 | 8 | 9 | 5 | 7 | 1 | 3 |

9 | 1 | 4 | 6 | 3 | 7 | 5 | 8 | 2 |

6 | 2 | 5 | 9 | 4 | 8 | 1 | 3 | 7 |

8 | 7 | 3 | 5 | 1 | 2 | 9 | 6 | 4 |

**Question 6.**

Find the missing number in the below-provided image?

**Solution:**

We can figure it out as 5 + 3 = 8, 8 * 2 = 16

In the same way 8 + 12 = 20, 20 * (2 + 2) = 80

34 + 27 = 61 * (4 + 3) = 61 * 7 = 427

Missing number = 16 + 21 = 37 * (7 + 4) = 37 * 11 = 407

∴ Missing number in the image is 407

**Question 7.**

Using four sevens (7) and a one (1) create the number 100. Except for the five numerals, you can use the usual mathematical operations (+, -, x, :), root, and brackets ().

**Solution:**

100 = 177 – 77

= (7 + 7) x (7 + (1 : 7))

So, (7 + 7) x (7 + (1 : 7)) = 14 x (7 + (1 : 7))

= 14 x ((49 + 1) : 7)

= 14 x (50 : 7)

= 2 x 50 = 100

**Question 8.**

Find the missing number?

5 | 7 | 6 |
---|---|---|

4 | 4 | 4 |

8 | 2 | ? |

**Solution:**

The simple trick is (5 + 7) / 2 = 6

(4 + 4) / 2 = 4

(8 + 2) / 2 = 10 / 2 = 5

∴ Missing number is 5.

**Question 9.**

What 5-digit number has the following property? If we put numeral 1 in front of the number, we get a number three times smaller, than if we put the numeral 1 behind this number.

**Solution:**

We can solve this by using an easy equation 3 (x + 100000) = 10x + 1

3x + 300000 = 10x + 1

10x – 3x = 300000 – 1

7x = 299,999

x = 299,999 / 7

x = 72,857

∴ 5-digit number is 72,857.

**Question 10.**

Find the digits x and y (x > y) such that the five-digit number 19x9y is divisible by 36.

**Solution:**

If a number is divisible by 36, then it is divisible by both 4 and 9.

Now, for 19x9y to be divisible by 4, we must have y = 2 or x = 6 (since the number formed by the last two digits must be divisible by 4).

Also, for 19x9y to be divisible by 9, the sum of the digits must be divisible by 9.

Therefore, when y = 2, then x = 6 and when y = 6, then x = 2.

Since, x > y, we have x = 6, y = 2.