How to learn to solve such problems?

Question

Mathematics

1) How to learn to solve problems like the ones below?
I believe that they need rather not a school curriculum of mathematics, but logic.
2) Are there tutorials teaching how to use logic and the ability to solve such problems?
"Igor noticed that among his subordinates there are no three people with the same last name, no three people with the same first name, and no three people with the same middle name. But every two have the same first name, or last name, or patronymic. What is the largest number of subordinates Igor?
"The bank has an even number of project teams. The first half has teams of 5 people, the other half has X people. All employees were asked how many project colleagues they had, and the average came out to be 16. Find X."
"There are a certain number of outstanding tasks in the list. Every day, the same number of new tasks are added to the list. It is known that 70 developers would complete all the tasks from the list in 24 days, and 30 developers in 60 days. How many developers would empty the list in 96 days? days?"
Here you can say just solve them as much as possible and that's it. But each of these tasks is unique . And each needs its own approach. This is not a discriminant, where the problem can be solved according to a ready-made template.

Answer 1

1 - logic. 2, 3 - stupid math, write an equation and solve. This was taught at school (Problems with pipes and a pool).
There is no specific algorithm for logical problems. It's like with, say, differential equations: technically, you know everything you need to solve, but understanding what, when and how to apply comes only with experience.
You will decide, read canonical solutions, delve into, find patterns, guess when which approach is better to apply (from basic tools for solving simple logical problems: the Dirichlet principle, invariant extraction, pattern detection, Venn diagrams, binary search ...)

Answer 2

Are you kidding me? My eight-year-old child solved the first two problems right off the bat
1. Two have the same first name, two have the same last name, two have the same patronymic as 6
2. (5-1)+(X-1)=16; X= 13
3. y+24x=1680
y+60x=1800
y+96x=96R

Answer 3

evgeniy_lm
1. Not true
Since they must have something in common in pairs, then 4 people.
In your case, the second two have neither common names nor common patronymics with the first.
2. Not true.
Everyone was asked => everyone in a team of 5 people said "4", and everyone in a team of x people said "x-1".
Let 2n be the number of commands.
Total people 5*n + x*n;
Everyone in a team of 5 said "4" => they named 5*4*n people.
Everyone in a team of x people said "x-1" => they named x*(x-1)*n people.
(5*4 + x*(x-1))/(5+x) = 16
20 + x^2 - x = 16(5+x)
x^2 - 17x - 60 = 0
to 20 people in other teams
https://nplus1.ru/news/2016/12/20/tinkoff

Answer 4

Greetings to MIPT graduates from NSTU graduates. Maybe useful to someone. Answers to the TCS test:
1. yes;
2.5;
3.4;
4.1008;
5.8;
6.17;
7.42;
8.-4;
9.20;
10.20.

Answer 5

Here you can say just solve them as much as possible and that's it. But each of these tasks is unique. And each needs its own approach. This is not a discriminant, where the problem can be solved according to a ready-made template.

So the trick is that if the template does not immediately give a ready-made answer, then this does not mean that it is useless. Solve or at least read the analysis of other people's solutions, read popular books and articles on mathematics, over time you will accumulate useful patterns and the ability to see which of them you can try to apply to a particular problem.
Here is a link I would recommend.