**Introduction to puzzles:**

A puzzle is a problem or enigma that tests the ingenuity of the solver. In a basic puzzle, one is intended to piece together objects in a logical way in order to come up with the desired shape, picture or solution. Puzzles are often contrived as a form of entertainment, but they can also stem from serious mathematical or logistical problems in such cases, their successful resolution can be a significant contribution to mathematical research.( Source Wikipedia.)

**Number solving puzzle 1:**

If 2 + 3 = 10

7 + 2 = 63

6 + 5 = 66

8 + 4 = 96

then what is the value of 5 + 3 =?

**Answer:** 40

**Explanation:**

2 + 3 = 5 Answer 5 is multiplied by first number 5 * 2 = 10

7 + 2 = 9 Answer 9 is multiplied by first number 9 * 7 = 63

6 + 5 = 11 Answer 11 is multiplied by first number 11 * 6 = 66

8 + 4 = 12 Answer 12 is multiplied by first number 12 * 8 = 96

So, 5 + 3 = 8 then this answer is multiplied by first number 8 * 5 = 40

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**Number solving puzzle 2:**

Find the next number in the given sequence : 0, 1, 1, 2, 3, 5, 8, ---

**Answer:** 13

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**Explanation:**

Because, 0 + 1 = 1

1 + 1 = 2

2 + 1 = 3

3 + 2 = 5

5 + 3 = 8

The term (starting with the third term) in the sequence is the sum of the two terms preceding it. The series is

called as Fibonacci series.

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**Number solving puzzle 3:**

Find the next number in the given sequence: 1, 3, 6, 10, ----

**Answer:** 15

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**Explanation:**

3 - 1 = 2; 6 - 3 = 3; 10 - 6 = 4;

Differences between the two consecutive numbers are 2, 3, 4

So, 15 - 10 = 5.

Alternatively, 1 + 2 = 3; 1 + 2 + 3 = 6; 1 + 2 + 3 + 4 = 10; 1 + 2 + 3 + 4 + 5 = 15;

The sequence of nth term is given by *n* (*n* + 1)/2.

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**Number solving puzzle 4:**

Find the next number in the given sequence : 2, 6, 14, _______, 62,

**Answer:** 30

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**Explanation: ** 6 - 2 = 4; 14 - 6 = 8; 30 - 14 = 16; 62 - 30 = 32; 126 - 62 = 64

Differences between the two consecutive numbers are 4, 8, 16, 32, 64, ..

(In this sequence where each number is multiplied by 2 and add by 2 to get the next number)

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**Number solving puzzle 5:**

Find the next number in the given sequence: 15, 12, 24, 20, 33, 28, 42 _______

**Answer:** 36

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**Explanation:** The odd terms of the given sequence is continually increase by 9, i.e.,

15 + 9 = 24; 24 + 9 = 33; 33 + 9 = 42; ...

The even terms of the given sequence is continually increase by 8, i.e.,

12 + 8 = 20; 20 + 8 = 28; 28 + 8 = 36;

**Number solving puzzle 6:**

Find the next number in the given sequence: 1, 2, 6, 24, __

**Answer:** 120

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**Explanation:** 1 = 1;

(1)(2) = 2;

(1)(2)(3) = 6;

(1)(2)(3)(4) = 24;

(1)(2)(3)(4)(5) = 120;

The sequence of nth term is given by *n*! (Factorial of n), That is product of all integers from 1 to n.

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**Number solving puzzle 7:**

Find the next number in the given sequence: 361, 289, 225, ___, 121

**Answer:** 169

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**Explanation:** In the given sequence each term squares of odd integers starting with the value is 19 in descending order.

19^{2} = 19 x 19 = 361; 17^{2} = 17 x 17 = 289; 15^{2} = 15 x 15 = 225; 13^{2} = 13 x 13 = 169; 11^{2} = 11 x 11
= 121;

Differences between the two consecutive numbers are 72, 64, 56, (In a given sequence starting with 72 and

continually decreasing by 8).

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**Number solving puzzle 8:**

Find the next number in the given sequence: 3, 10, 20, 27, _______, 44

**Answer:** 37

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**Explanation: ** In the given sequence odd terms continually increase by 17, i.e., 3, 20, 37 …

In the given sequence even terms also continually increase by 17, i.e., 10, 27, 44 ...

otherwise, add 7 and 10 alternately starting with 3.

Between, if you have problem on these topics Equivalent Fraction Chart, please browse expert math related websites for more help on Complex Number Formulas.

**Number solving puzzle 9:**

Find the next number in the given sequence: 1, 3, 7, 15, 31,

**Answer:** 63

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**Explanation: ** 2^{1} - 1 = 2 - 1 = 1;

2^{2} - 1 = 4 - 1 = 3;

2^{3} - 1 = 8 - 1 = 7;

2^{4} - 1 = 16 - 1 = 15;

2^{5} - 1 = 32 - 1 = 31;

2^{6} - 1 = 64 - 1 = 63;

The sequence n th term is given by 2* ^{n}* - 1.

So, Difference between the two consecutive numbers forms sequence is: 2, 4, 8, 16, 32, 64,

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**Number solving puzzle 10:**

Find the next number in the given sequence. 120, 24, 6, 2, __

**Answer:** 1

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**Explanation:** (1)(2)(3)(4)(5) = 120;

(1)(2)(3)(4) = 24;

(1)(2)(3) = 6;

(1)(2) = 2;

(1)(1) = 1