To date, there is no universal test to determine the level of human intelligence. Therefore, in many specialized educational institutions, teachers give students simple, at first glance, tasks that quickly separate grains from the chaff and determine the group of students with the most flexible thinking.
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The following tasks in one form or another are used by professors of Western (primarily American) universities, and a fairly small part of students even in technical specialties is able to solve them all in the allotted time. In fact, every adult can give the right answers, the only question is how much time and effort it will take. We offer readers to go through the quick express intellect right now and solve the problems below with an approximate rating scale:
1. Decided / a in 10 or less minutes in the mind – a genius;
2. Decided / a in more than 10 minutes or on paper – techie;
3. Did not decide at all – the humanist.
Answers to problems with solutions will be given at the end of the article.
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A man infected with a new respiratory virus, which spreads exponentially exponentially, arrived in one little-known Chinese city – twice as many people are infected every day than it was the day before (1, 2, 4, 8, 16, etc.). Exactly 36 days later, the entire population of the city was infected.
Question: how many days would all the inhabitants of the city get sick if 2 infected people originally came to it?
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The online store sells a tablet with a stylus for the promotion, the total cost is $ 110, while it is known that the tablet itself is $ 100 more expensive than the stylus.
Question: How much does a stylus cost?
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In 2030, Microsoft and Google decided to buy Apple. Microsoft did not have enough $ 200 billion to complete the deal, and Google did not have enough – $ 140 billion. Then Microsoft and Google decided to combine the assets, but even then they did not have enough $ 40 billion.
Question: What is the price of Apple?
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Three 3D printers can print three triangles in three minutes.
Question: In how many minutes 100 of the same 3D printers will print 100 triangles?
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Kolya lives on the fourth floor in a house without an elevator and each time goes through 120 steps, going up home. Petya lives on the second floor in the same house.
Question: how many steps does Petya walk?
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To separate the task block from the answer block, we will place an interesting mathematical focus between them, which introduces most viewers into a stupor and does not require complex arithmetic calculations from the performer.
The essence of the trick:
For all, the viewer writes down an arbitrary 4-digit number (for example, 5432), the performer immediately writes his prediction number on another sheet and hides the paper with the prediction in his pocket. Then the viewer and performer alternately add two 4-digit numbers to the original, receiving approximately the following picture:
1) 5432 – the initial number of the viewer;
2) 7523 – the number added by the viewer;
3) 2476 – the number added by the performer (magician);
4) 6814 – the number added by the viewer;
5) 3185 – the number added by the performer (magician).
Then the viewer sums up all the recorded numbers on the calculator and gets the number 25430, the performer takes out the paper with the prediction from his pocket and it, of course, coincides with the received amount – 25430.
A moment of misunderstanding for the viewer in this focus is the fact that three of the five numbers in the total amount were just invented by him, which means that it seems to him that it was impossible to predict the result. However, in fact, the contractor quite easily controls the total amount. If you look at pairs of numbers in 2-3 and 4-5 lines, their sums will be equal to 9999 (7523 + 2476 = 9999, 6814 + 3185 = 9999), which, of course, is not accidental. Adding the numbers after the viewer, the performer simply substitutes the necessary numbers to get nine:
For example, the viewer recorded 7523, which means the performer writes 2 (2 + 7 = 9) 4 (5 + 4 = 9) 7 (2 + 7 = 9) 6 (3 + 6 = 9) = 2476 to get 7523 + 2476 = 9999;
That is, the sum of the last four numbers will always be equal to 9999 + 9999 = 19 998 = 20,000 – 2. Accordingly, to make a prediction, the performer just needs to add 20,000 to the first recorded by the viewer and subtract 2. In our example, 20,000 + 5432 – 2 = 25432 – 2 = 25430.
Answers to tasks
Answer: 35 days
The easiest way to realize this answer is through visual perception through writing on paper progressions in both cases (with one and two “zero” patients):
1 day – 1 patient;
2 day – 2 patients; 1 day – 2 patients;
3 day – 4 patients; 2 day – 4 patients;
4 day – 8 patients; 3 day – 8 patients;
5 day – 16 patients, etc. 4 day – 16 patients, etc.
That is, if there were two infected at once, then it is necessary one day less than would be the case with one infected.
Answer: 5 dollars
Naturally, the brain is trying to suggest an obvious and incorrect answer – $ 10. However, then we get the price of the tablet (100 dollars more expensive than the stylus) equal to 110 dollars, and the total purchase price then will be 110 + 10 = 120 dollars.
Answer: $ 300 billion
The easiest way is to solve this problem head-on-paper by writing three simple equations of the form: x + 200 = S, y + 140 = S and x + y = S – 40 and replacing some variables with expressions of others.
However, people with flexible thinking solve this problem more elegantly:
Just imagine that Google simply transferred its money to buy Apple from Microsoft. The latter was initially lacking $ 140 billion, and after receiving the money Google was only short of $ 40 billion. Accordingly, Google had an asset of $ 100 billion and it also lacked 200 billion for Apple to buy on its own. Accordingly, the price of Apple = $ 300 billion.
Answer: 3 minutes
It is easy to calculate that one 3D printer prints one triangle in 3 minutes. So 100 units will produce 100 units in the same 3 minutes.
Answer: 40 steps
Climbing to the 4th floor, Kolya overcomes three flights of stairs, respectively, one flight of stairs consists of 120/3 = 40 steps. Climbing to the second floor, Petya passes only one passage, that is, 40 steps.