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 puzzles 1 to 5:

 

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

 

Number solving puzzle 2:

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

Answer: 13

 

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.

 

Number solving puzzle 3:

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

Answer: 15

 

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.

 

Number solving puzzle 4:

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

Answer:  30

 

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)

 

Number solving puzzle 5:

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

Answer: 36 

 

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 puzzles 6 to 10:

 

Number solving puzzle 6:

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

Answer:  120

 

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.

 

Number solving puzzle 7:

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

Answer: 169

 

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

192 = 19 x 19 = 361;   172 = 17 x 17 = 289;   152 = 15 x 15 = 225;   132 = 13 x 13 = 169;   112 = 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).

 

Number solving puzzle 8:

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

Answer: 37

 

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  

 

Explanation:            21 - 1 = 2 - 1 = 1;

                               22 - 1 = 4 - 1 = 3;

                               23 - 1 = 8 - 1 = 7;

                               24 - 1 = 16 - 1 = 15;

                               25 - 1 = 32 - 1 = 31;

                               26 - 1 = 64 - 1 = 63;

The sequence n th term is given by 2n - 1.

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

 

Number solving puzzle 10:

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

Answer: 1

 

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

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

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

                        (1)(2) = 2;

                        (1)(1) = 1