Puzzles and Mathematical Patterns. How to recognize them. Part I by @josegnzalito
Good evening, friends Steemians, this time I want to share with you some knowledge that I have been learning in solving riddles and mathematical puzzles where logic and deduction must be applied for their resolution.
In this publication I will cover the simplest elements to recognize the patterns that are presented in some puzzles and that will help us to achieve their solution. As I publish about it, the level of difficulty and complexity will increase. For the moment we will start with the basics.
Bees build their combs following mathematical patterns. Fuente.
Order.
This type of situation occurs when the data that is supplied maintains a sequence that can be recognizable and evident, both ascending or descending. We can observe it in numbers (1, 2, 3, 4 ...), in the alphabet (a, b, c, d ...) and also in geometric figures (Triangle, Square, pentagon, hexagon ... ).
For example we have the following numbers
1,3,5,7 ....
the next in the sequence would be 9 and 11, since these are evidently increasing by 2 by 2.
d, f, h, j ...
the next letters would be l and n, since the sequence is ascending and skipping a letter in between. After the d, the e is skipped, after the f the g is skipped, and so on.
Repeat Pattern.
Perhaps those of this type are the most common, where patterns are formed that we must detect as the riddles are presented to us.
They exist from the simplest:
1,2,3,1,2,3,1,2,3 ...
Here we can see the pattern of repeating 1, 2, 3.
Even some more complex
9, 98, 987, 9876, 98765 ...
In this we observe that each number includes another digit, which also decreases, so the following numbers follow the pattern and would be 987654 and 9876543.
Fractals are infinite mathematical patterns. Fuente.
Alternating.
In this type of sequence we will find 2 or more mixed or interlaced repetitive patterns. For example, let's look at patterns 1, 2, 3, 4 and A, B, C, D.
then they can be combined into a single alternating pattern that would look like 1, A, 2, B, 3, C, 4, D.
and in this way they become more complex:
We use a sequence of odd numbers 1, 3, 5, 7, 9 and combine it with a sequence of letters b, d, f, h, j the result would be
1, b, 3, d, 5, f, 7, h, 9, j ...
the next thing in the sequence, according to the pattern, would be 11, i.
The first pattern of this alternate sequence Increase each number by four: 4, 8, 12, 16 ... The second pattern subtracts three: 36, 33, 30, 27 ...
4, 36, 8, 33, 12, 30, 16, 27, 20, 24 ...
The next two numbers are 20 (adding 4 to 16) and 24 (subtracting 3 from 27).
Let's practice everything we have learned.
7, __ , 11, __ , __ , 17, 19.
5, __ , 15, __ , __ , 30, __, 40.
__, 600, 700, __, 900, __ , __ , 1200.
25, 50, __, __ , 125, __ , 175.
__ , 65, 77, __, __, 113, __ , 137.
b, d, f, __ , j, __, __, p.
c, g, k, __, s.
15, __, 13, __, 11, __, __, 8.
__, 27, 24, 21, __, 15, __.
125, __, 115, __, __, 100, __, 90.
__, 1075, 1050, __, __, __, 950, 925.
__ , w, v, __, t, s, r.
q, __, m, __, i, __, e, c.
y, v, __, p, __, __, g, d.
8, 2, 8, 8, 2, 8, 8, 8, 2, 8, 8, 8, 8, 2, 8, 8, 8, __, __.
6, __, 888, __, 1010101010, 111111111111, 12121212121212,
2, 23, 234, 2345, __, __.
1, 31, __, 7531, 97531, 1197531, __.
11, 99, 22, 88, __, __, 44, 66, __, __, 66, 44.
3, 18, 6, 16, 9, 14, 12, 12, __, __, __.
6, 24, 12, __, __, 24, 24, 24, 30, __.
5, 6, 7, 9, 9, 12, 11, 15, __, __, __.
10, 50, 15, 40, 20, 30, 25, __, __, __.
p, q, o, r, n, s, m, __, __, __.
__, __, __, __, V, P, T, Q, R, R, P.
I will grant to have 5 Steems to distribute them among all those steemians who share in a comment in this post their results to the proposed exercises.
Thanks to the support of @tarpan and @zero-to-infinity
Twitter.
It took my almost 20 minutes to get all the answers
(1). 7, 9 , 11, 13 ,15 , 17, 19.
(2). 5, 10 , 15, 20 , 25 , 30, 35, 40.
(3). 500, 600, 700, 800, 900, 1000, 1100 , 1200.
(4). 25, 50, 75, 100 , 125, 150 , 175.
(5). 53, 65, 77, 89, 101, 113, 125 , 137.
(6). b, d, f, h , j, l, n, p.
(7). c, g, k, o, s.
(8). 15, 14, 13, 12, 11, 10, 9, 8.
(9). 30, 27, 24, 21, 18, 15, 12.
(10). 125, 120, 115, 110, 105, 100, 95, 90.
(11). 1100, 1075, 1050, 1025,1000, 975, 950, 925.
(12). x, w, v, u, t, s, r.
(13). q, o, m, k, i, g, e, c.
(14). y, v, s, p, m, j, g, d.
(15). 8, 2, 8, 8, 2, 8, 8, 8, 2, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8.
(16). 6, 77, 888, 9999, 1010101010, 111111111111, 12121212121212.
(17). 2, 23, 234, 2345, 23456, 234567.
(18). 1, 31, 531, 7531, 97531, 1197531, 131197531.
(19). 11, 99, 22, 88, 33, 77, 44, 66, 55, 55, 66, 44.
(20). 3, 18, 6, 16, 9, 14, 12, 12, 14, 10, 16.
(21). 6, 24, 12, 24, 18, 24, 24, 24, 30, 24.
(22). 5, 6, 7, 9, 9, 12, 11, 15, 13, 18, 15.
(23). 10, 50, 15, 40, 20, 30, 25, 20, 30, 10.
(24). p, q, o, r, n, s, m, t, l, u.
(25). Z, N, X, O, V, P, T, Q, R, R, P.
1). 7, 9 , 11, 13 ,15 , 17, 19.
2). 5, 10 , 15, 20 , 25 , 30, 35, 40.
3). 500, 600, 700, 800, 900, 1000, 1100 , 1200.
4). 25, 50, 75, 100 , 125, 150 , 175.
5). 53, 65, 77, 89, 101, 113, 125 , 137.
6). b, d, f, h , j, l, n, p.
7). c, g, k, o, s.
8). 15, 14, 13, 12, 11, 10, 9, 8.
9). 30, 27, 24, 21, 18, 15, 12.
10). 125, 120, 115, 110, 105, 100, 95, 90.
11). 1100, 1075, 1050, 1025,1000, 975, 950, 925.
12). x, w, v, u, t, s, r.
13). q, o, m, k, i, g, e, c.
14). y, v, s, p, m, j, g, d.
15). 8, 2, 8, 8, 2, 8, 8, 8, 2, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8.
16). 6, 77, 888, 9999, 1010101010, 111111111111, 12121212121212.
17). 2, 23, 234, 2345, 23456, 234567.
18). 1, 31, 531, 7531, 97531, 1197531, 131197531.
19). 11, 99, 22, 88, 33, 77, 44, 66, 55, 55, 66, 44.
20). 3, 18, 6, 16, 9, 14, 12, 12, 14, 10, 16.
21). 6, 24, 12, 24, 18, 24, 24, 24, 30, 24.
22). 5, 6, 7, 9, 9, 12, 11, 15, 13, 18, 15.
23). 10, 50, 15, 40, 20, 30, 25, 20, 30, 10.
24). p, q, o, r, n, s, m, t, l, u.
25). Z, N, X, O, V, P, T, Q, R, R, P.