Number Puzzles Reasoning

Clearly, sum of numbers in each row is 17.
So, missing number = 17 – (4 +7) = 6.

This is a multiplication magic square. The product of each set of three numbers in any column or row is the constant 120.

In the first row, ,
In the second row, , .
∴ In the third row, missing number =

In the first row, 72 ÷ = 6.
In the second row, 96 ÷ = 12.
Let the missing number in the third row be x.
Then, 108 ÷ = 18
⇒ = = 6
⇒ x = 12

In the first row, (263 – 188) × 4 = 300.
∴ In the second row, missing number
= (915 – 893) × 4 = 22 × 4 = 88.

In the first row, =
In the second row,
Let the missing number in the third row be x. Then,
⇒ ⇒ x = 12.

In each row, the second number is the square of the first number, and the third number is the square of the number obtained by interchanging the digits of the first number.
∴ Missing number = (91)2 = 8281.

Clearly, (1st row)³ + (2nd row)³ + (3rd row)³ = 4th row
So, in the first column,
2³ + 1³ + 3³ = 8 + 1 + 27 = 36
In the third column,
0³ + 4³ + 3³ = 0 + 64 + 27 = 91
∴ In the second column, missing number
= 4³ + 2³ + 1³ = 64 + 8 +1 = 73

Clearly, (1st row)² + (2nd row)² + (3rd row)² = 4th row.
Thus, in the first column, 4² + 2² + 1² = 21.
In the second column, 5² + 3² + 8² = 98.
∴ In the third column, missing number
= 6² + 7² + 3² = 36 + 49 + 9 = 94.

In the first column, 6 × 5 × 4 = 120.
In the second column, 6 × 7 × 3 = 126
Let the missing number be x . Then in the third column, we have :
8 × 5 × x = 320
⇒ x = ³²⁰⁄₄₀ = 8.

In the first column,(5 + 8 + 7) ÷ 4 = 5.
In the second column, (9 + 6 + 13) ÷ 4 = 7.
In the fourth column, (7 + 10 + 19) ÷ 4 = 9.
Let the missing number be x. Then, in the third column, we have : (8 + 9 + x) ÷4 = 8
⇒ 71 + x = 32 ⇒ x =15.

The sum of the numbers in each column is 200.
∴ Missing number = 200 – (87 + 56 + 50) = 7.

The numbers in the right half form the series :
2, 3, 4, 5.
The numbers in the left half form the series :
5, 7, 9, 11.

Start at 2 and, working clockwise, jump three spaces each time adding 3.

Moving clockwise,
we have : 594 ÷ 3 = 198 : 198 ÷ 3 = 66.
So, missing number = 66 ÷ 3 = 22

Clearly, (5 – 4)³ = 1;
(7 – 3)³ = 64; (11 – 8)³ = 27.
So, missing number = (8 – 2)³ = 6³ = 216.

The given figure contains numbers 1 to 6 in three alternate segments, the smaller number being towards the outside and the numbers 14 to 19 in the remaining three alternate segments with the smaller number towards the inside.

Clearly, we have :
7 × 2 + 2 = 16; 16 ×2 + 2 = 34 and so on.
so missing number = 34 ×2 + 2 = 70

The number inside the triangle is obtained by dividing the product of the numbers outside of the triangle by 10. Thus,
In I triangle, (5 × 6 × 4) ÷10 = 12
In II triangle, (6 × 7 × 5) ÷10 = 21
∴ In III triangle, missing number
= (4 × 8 × 10) ÷ 10 = 32.

In fig. (A), 93 – (27 + 63) = 3
In fig, (B), 79 – (38 + 37) = 4
∴ In fig. (C), missing number = 67 – (16 + 42) = 9.

The number inside the circle is equal to the difference between the sum of the numbers at the extremities of the horizontal diameter and the sum of numbers at the extremities of the vertical diameter.
In fig. (A), (5 + 6) – (7 + 4) = 0
In fig. (B), (7 + 6) – (8 + 4) = 1.
∴ In fig. (C) missing number = (11 + 2) – (0 + 2) = 11

The number inside the circle is the difference of the numbers on its left and right.

The number at the centre is to be multiplied by 1, 2, 3, and 4, then subtract ‘1’ from each to get the peripheral number.

Multiply all the numbers around the circle and then divide it by 10 to get the number at the centre, viz.,

In fig. (A),
(101 + 15) – (35 + 43) = 116 – 78 = 38.
In fig. (B), Missing number
= (48 + 184) – (56 + 34) = 232 – 90 = 142.

Clearly, we have : 15 × 2 = 30, 2 × 7 = 14, 7 × 9 = 63
So, missing number = 9 × 15 = 135.

The sum of numbers at the extremities of the three line segments in each figure is same.
In fig. (A), 39 + 33 = 29 + 43 = 27 + 45 = 72
In fig. (B), 42 + 31 = 29 + 44 = 30 + 43 = 73
Let the missing number in fig. (C) be x.
Then, x + 10 = 59 + 20 = 40 + 39 = 79 or x = 69.

The digits of the number inside the circle are the differences between the corresponding numbers above and below the circle. Thus,
In fig. (A), 1 = (2 – 1), 3 = (6 – 3), 1 = (5 – 4).
In fig. (B), 2 = (4 – 2), 4 = (6 – 2), 8 = (8 – 0)
So, in fig. (C), the digits of the missing number are :
(7 – 5), (9 – 3), (3 – 1) i.e., 2, 6, 2.
∴ Missing number = 262.

In fig. (A), (915 – 364) = 551.
In fig. (B), (789 – 543) = 246.
∴ In fig. (C), missing number = (863 – 241) = 622.

In fig (A), 6² = 36, 8² = 64, 5² = 25, 7²
= 49 and 6 + 8 +5 + 7 = 26
In fig (B), 3² = 9, 5² = 25, 4² = 16, 9² = 81.
and 3 + 5 + 4 + 9 = 21
In fig (C), 5² = 25, 12² = 144, 6² = 36, 8² = 64.
So, missing number = 5 + 12 + 6 + 8 = 31.

In fig (A), (3 × 3) + (6 × 5) = 39
In fig (B), (4× 4) + (5 × 7) = 51
∴ In fig (C), missing number
= (3 × 4) + (5 × 5) = 37

The arrangement is as follows :
In fig. (A), (3² + 6²) – (2² + 4²) = (9 + 36) – (4 + 16)
= 45 – 20 = 25
In fig. (B), (7² + 11²) – (8² + 6²) = (49 + 121) – (64 + 36)
= 170 – 100 = 70
In fig. (C), let the missing number be x.
Then, (1² + 4²) – (5² + x²) = –12
or 17 + 12 = (52 + x2) or x² = 29 – 25 = 4
or x = 2

In fig. (A), (6 × 3) + (5 × 15) = 18 + 75 = 93.
In fig. (C), (4 × 8) + (18 × 1) = 32 + 18 = 50.
∴ In fig. (B), missing number
= (9 × 6) + (7 × 5) = 54 + 35 = 89.

In fig. (A), (16 – 6)² + (5 – 2)² = 10² + 3² = 109.
In fig. (B), (22 – 15)² + (21 – 19)²
= 7² + 2² = 53.
∴ In fig. (C), missing number
= (17 – 13)² + (51 – 48)² = 4² + 3² = 25.

The lower number is obtained by adding the square of the upper two numbers. Thus,
In fig. (A), 2² + 4² = 20
In fig. (B), 3² + 9² = 90
∴ In fig. (C), missing number = 1² + 5² = 26

The above three numbers are multiples of the number at the bottom.
Clearly, 36, 18 and 27 are all multiples of 9.
So, the missing number is 9.

Putting A = 1, B = 2, C = 3, D = 4 ... X = 24, Y = 25, Z = 26,
We have F + P = 6 + 16 = 22 : G + N = 7 + 14 = 21
: J + E = 10 + 5 = 15.
Since K = 11, so value corresponding to missing letter
= (27 – 11) = 16
So, the missing letter is the 16th letter of the English alphabet, which is P.

This way, the sum of the numbers in the same shape total 33.

We have (56 + 15) – (22 + 8)
= 41, (46 + 9) – (10 + 6) = 39
So, missing number = (34 + 11) – (14 + 6) = 25.

We have : 3 × 5 + 1 = 16 ,
16 × 5 + 1 = 81, 81 × 5 + 1 + 1 = 406.
So , missing number = 406
406 × 5 + 1 = 2031.

The arrangement is :5 + 3 = 8, 8 + 4 = 12, 12 + 1 = 13.
So, the missing number is 12.

The above three numbers are multiples of the number at the bottom. Clearly 36, 18 and 27 are all multiples of 9. So, the missing number is 9.

The sum of the two numbers in the upper part is 7 times the number in the lower part.
So, missing number = (89 + 16) + 7 = 15.

We have : (3 × 4 × 2 × 5) ÷ 10 = 12 ;
(6 × 2 × 3 × 5) ÷ 10 = 18.
So, missing number = (2 × 2 × 9 × 5) ÷ 10 = 18

We have : (5 x 3) + (6 x 8) = 63, (2 x 7) + (3 x 9) = 41
So, missing number = (6 x 7) + (8 x 5)
= (42 + 40) = 82.

We have : + + + = 26 ;
+ + + = 21
So, missing number
= + + +
= (5 + 12 + 6 + 8) = 31

We have (15 – 5) (2 + 6) = 80, (9 – 4) (7 + 6) = 65
So, missing number = (13 – 11 ) x (16 + 8) = 48.

The number inside the circle is obtained by multiplying the sum of the upper number, the lower number and the number corresponding to the position of the letter in the english alphabet, by the number on the right and then subtracting the number on the left from the product.
Thus we have (2 + C + 5) x 3 – 4 = (2 + 3 + 5) x 3 – 4 = 26 ; (4 + H + 4) x 5 – 10 = (4 + 8 + 4) x 5 – 10 = 70.
Let the missing number be x.
Then (8 + J + 6) × x – 6 = 90
⇒ (8 + 10 + 6) × x = 96 ⇒ x = 4.

The letter in the second column is three steps behind that in the first column, and the letter in the third column is four steps behind that in the second column. So, the missing letter in the first row will be three steps behind Z, which is W. The missing letter in the second row will be four steps behind O, which is K. The missing letter in the third row will be three steps ahead of G, which is J.

The letters in the first row follow the sequence + 5, + 7.
The letters in the second row follow the sequence + 6, + 8.
In the third row, the first letter G moves 7 steps forward to give the second letter N. Clearly, the missing letter will be 9 steps ahead of N i.e., W.

Putting A = 1, B = 2, C = 3, ......., M = 13, ....., X = 24,
Y = 25, Z = 26, we have :
In the first column, F – A = 6 – 1 = 5 = E.
In the second column, W – J = 23 – 10 = 13 = M.
∴ In the third column, missing letter
= O – K = 15 – 11 = 4 = D.

Consecutive letters occupy alternate positions in each row.

The letters in the first row form a series C, D, E (a series of consecutive letters). The letters in the second row form a series I, K, M (a series of alternate letters). Similarly, the letters in the third row will form the series D, G, J (a series in which each letter is three steps ahead of the previous one). So, the missing letter is G. Also, the number in the second column is equal to the product of the numbers in the first and third columns.
So, missing number is (4 × 7) i.e., 28.
Thus, the answer is 28G.

In each row, out of the letters A, B and C, each of these must appear one. Also, in each column. The product of first and third numbers is equal to the second numbers so, the missing number will be (2 x 4) i.e., 8 and the missing letter will be C. Thus, the answer is 8C.

We have: 4 × 2 – 1 = 7,
7 × 2 + 1 = 15,
15 × 2 – 1 = 29,
29 × 2 + 1 = 59,
59 × 2 – 1 = 117,
117 × 2 + 1 = 235.
So missing number
= 235 × 2 – 1 = 469.