1. 4 X 4 Puzzle

Solution:

How to Solve?
First, let us learn the rules -
1. Each row and column can have numbers 1 to 4 only.
2. No number can be repeated in a row.
3. No number can be repeated in a column.
4. Similarly, each sub-grid (with dark borders) can have numbers 1 to 4 but no number can be repeated in a sub-grid.

2. 4 X 4 Puzzle

Solution:

3. 4 X 4 Puzzle

Solution:

4. 4 x 4 Puzzle

Solution:

5. 4 X 4 Puzzle

Solution:

6. 4 X 4 Puzzle

Solution:

1. Find the missing number.

Solution:

In the given puzzle,
5 × 8 = 40
5 × 6 = 30
8 × 3 = 24
6 × 3 = 18
Therefore, the missing number is 18.

2. Identify the number to be written in the empty place.

Solution:

In the given puzzles, the sum of three numbers (both in columns and rows) is 15.
8 + 3 + 4 = 15
6 + 7 + 2 = 15
8 + 1 + 6 = 15
3 + 5 + 7 = 15
Let x be the missing number.
4 + x + 2 = 15
6 + x = 15
x = 15 – 6 = 9
Hence, the required number is 9.

3. Observe the following and find the missing value.

Solution:

The given maths puzzle has the following pattern.
5 × 8 = 40
82 = 8 × 8 = 64
7 × 9 = 63
92 = 9 × 9 = 81
4 × 4 = 16

42 = 4 × 4 = 16
Therefore, the missing number is 16.

4. What is the missing number in the following puzzle?

Solution:

In the given puzzles, the sum of two numbers in the opposite portions is the same.
11 + 13 = 24
7 + 17 = 24
8 + 16 = 24
4 + ? = 24
? = 24 – 4 = 20
Thus, the missing number is equal to 20.

5. Complete the following puzzle.

Solution:

Let p and q be the two numbers in the first row.
Let r and s be the two numbers in the second row.
p + q = 8….(1)
r – s = 6….(2)
p + r = 13….(3)
q + s = 8….(4)
Subtracting (3) from (1), we get;
p + q – (p + r) = 8 – 13
q – r = -5….(5)
Subtracting (4) from (1), we get;
p + q – (q + s) = 8 – 8
p – s = 0
i.e., p = s
Adding (2) and (4), we get;
r – s + q + s = 6 + 8
r + q = 14….(6)
Adding (5) and (6), we have;
q – r + r + q = -5 + 14
2q = 9
q = 9/2 = 4.5
Substituting q = 4.5 in (1),
p + 4.5 = 8
p = 8 – 4.5 = 3.5
So, s = 3.5
Substituting q = 4.5 in (6),
r + 4.5 = 14
r = 14 – 4.5 = 9.5
Hence, the complete puzzle is given as:

6. What can be added in place of a question mark?

Solution:

Let us consider the lower part of the given puzzle.
4 = 2²
49 = 7²
14 = 2 × 7
A similar pattern exists in the remaining parts too.
Now, consider the right part.
49 = 7²
35/7 = 5
5² = 25
That means 7 × 5 = 35.
Thus, the missing number is 25.

7. Find the number that can be replaced with (?) in the following puzzle.

Solution:

In the given puzzle, 4
24 = 4 × 6
6
576 = 24 × 24
And
3
15 = 3 × 5
5
15 × 15 = 225
Hence, 225 can be written in the missing place.

8. What will replace the (?) in the following puzzle?

Solution:

In the given puzzle,
6 × 7 = 42
3 × 7 = 21
? × 7 = 63
? = 63/7 = 9
Therefore, 9 should be written in place of a question mark.

9. Using four 9s and one 1, form any numerical expression such that it results in 100.

Solution:

Number of 9s = 4
i.e., 9, 9, 9, 9
Number of 1s = 1
Required numerical expression = 199 – 99 = 100

10. Consider the following:

A + B = 15
B × C = 84
C ÷ 4 = 3
B + D = 18
Find the value of D.

Solution:

Solution:
Given,
A + B = 15
B × C = 84
C ÷ 4 = 3
B + D = 18
Consider C ÷ 4 = 3.
C/4 = 3
C = 3 × 4 = 12
Now, B × C = 84
B × 12 = 84
B = 84/12 = 7
From the given,
A + B = 15
A + 7 = 15
A = 15 – 7 = 8
Also, B + D = 18
7 + D = 18
D = 18 – 7 = 11

9. Can you solve this puzzle in 5 minutes?

Solution:

A1 + A2 = 14
A1 + A3 = 15
A2 + A4 = 16
A3 – A4 = 10
Next, we A1 + A2 + A1 + A3 + A2 + A4 + A3 - A4 = 14+15+16+10
=> A1+ A2 + A1 + A3 + A2 + A3 = 14 + 15 + 16 + 10
=> 2 (A1 + A2 + A3) = 14 + 15 + 16 + 10
=> A1 + A2 + A3 = (14 + 15 + 16 + 10)/ 2 = 55/2 = 27.5
So, now we have A1 + A2 + A3 = 27.5
=> A3 = 27.5 – (A1 + A2)
=> A3 = 27.5 – 14 = 13.5
Hence, A3 = 13.5
Similarly,
=> A2 = 27.5 – (A1 + A3)
=> A2 = 27.5 – 15 = 12.5
Hence, A2 = 12.5
Now we find out A1
=> A1 + A2 = 14 (as per figure)
=> A1 = 14 – A2
=> A1 = 14 – 12.5 = 1.5
Hence, A1 = 1.5
Now we find out A4
=> A3 – A4 = 10 (as per figure)
=> A4 = A3 – 10
=> A4 = 13.5 – 10 = 3.5
Hence, A4 = 3.5
To summarize, we got A1 = 1.5, A2 = 12.5, A3 = 13.5, A4 = 3.5

10. Find a solution for each of the trees below! There are many possibilities! The first tree has been completed for you.

Solution:

Tree 1: 2 + 7 = 9; 7 + 5 = 12; 9 + 12 = 21;
Tree 2: 5 + 4 = 9; 4 + 2 = 6; 9 + 6 = 15;
Tree 3: 3 + 8 = 11; 8 + 4 =12; 11 + 12 = 23;
Tree 4: 5 + 3 = 8; 3 + 1 = 4; 8 + 4 = 12;
Tree 5: 4 + 5 = 9; 9 + 6 = 15; 2 + 4 = 6;
Tree 6: 6 + 3 = 9; 9 + 11 = 20; 3 + 8 = 11;

13. Can you put the numbers 1 to 8 in each of the squares so that each side adds up to the middle number?

Solution:

14. Can you join all nine dots with four straight lines, without taking your pencil off the paper? You can not go over any line twice.

Solution:

15. Put the numbers 1,2,3,4,5,6 and 7 in the circles so that each straight line of three numbers adds up to the same total.

Solution:

16. Using any whole numbers as manytimes as you like make each line of the rectangle add up to 20.

Solution: