Update

exercises.md

@@ -116,21 +116,22 @@ Here are some questions to test your LRS related knowledge :D
 15. Name at least five licenses commonly used for [FOSS](foss.md) programs, five text editors/IDEs commonly used for programming and five operating systems whose source code is mostly free-licensed (none of these is allowed to be using the same or forked kernel of any other).
 16. What is the minimum number of [bits](bit.md) that will allow us to represent 12345678910111213 distinct values?
 17. Give at least one example of [analog](analog.md) electronic device and one of [digital](digital.md) mechanical device.
-18. Find a normalized (having length 1) [normal](normal.md) ([vector](vector.md) that's perpendicular to surface) of the [triangle](triangle.md) defined by vertices *A = {1,2,3}*, *B = {5,5,1}* and *C = {1,5,2}*. (Orientation doesn't matter.)
-19. Why will (in a typical programming language such as C) an infinite [recursion](recursion.md) crash the program but infinite loop generally won't?
-20. Answer yes/no to following: Is base-three number 2101 greater than base-seven number 206? Is [gemini](gemini.md) better than [gopher](gopher.md)? Is there any [triangle](triangle.md) (in Euclidean geometry) whose one side is longer than the sum of lengths of its other two sides?
-21. There are two walls 2 meters apart, the right wall is moving left by the speed 0.1 m/s, the left wall is moving right by the same speed 0.1 m/s. There is a fly in the middle between the walls, flying by speed 1 m/s. It is flying towards one wall, then when it reaches it it turns around and flies towards the other wall etc. When the walls completely close in, what distance would the fly have traveled? (There is a simple solution.)
-22. Solve these [anagrams](anagram.md): *no cure sir*, *come piss ron*, *ginger*, *nicer shops*, *fog tag*, *trek now*.
-23. At what times, with precision to seconds, do clock hands overlap (just compute AM, PM is the same)?
-24. In 3D computer [graphics](graphics.md) what's the difference between [shading](shading.md) and drawing [shadows](shadow.md)?
-25. Can we say that the traditional feed forward [neural networks](neural_network.md) are [Turing complete](turing_complete.md)? Explain why or why not.
-26. Wicw mx uum yvfe bbt uhmtf ok?
-27. What is the *Big O* time [complexity](complexity.md) of worst case scenario for [binary search](binary_search.md)?
-28. Does the statement "10 does not equal 10" logically [imply](implication.md) that intelligent alien life exists?
-29. What is the principle of [asymmetric cryptography](asymmetric_cryptography.md) and why is it called *asymmetric*?
-30. What is the main reason for [Earth](earth.md) having seasons (summer, winter, ...)?
-31. WARNING: VERY HARD. There are two integers, both greater than 1 and smaller than 100. *P* knows their product, *S* knows their sum. They have this conversation: *P* says: I don't know the numbers. *S* says: I know you don't, I don't know them either. *P* says: now I know them. *S* says: now I know them too. What are the numbers? To solve this you are allowed to use a programming language, pen and paper etc. { Holy shit this took me like a whole day. ~drummyfish }
-32. Did you enjoy this quiz?
+18. Is physical violence every justified?
+19. Find a normalized (having length 1) [normal](normal.md) ([vector](vector.md) that's perpendicular to surface) of the [triangle](triangle.md) defined by vertices *A = {1,2,3}*, *B = {5,5,1}* and *C = {1,5,2}*. (Orientation doesn't matter.)
+20. Why will (in a typical programming language such as C) an infinite [recursion](recursion.md) crash the program but infinite loop generally won't?
+21. Answer yes/no to following: Is base-three number 2101 greater than base-seven number 206? Is [gemini](gemini.md) better than [gopher](gopher.md)? Is there any [triangle](triangle.md) (in Euclidean geometry) whose one side is longer than the sum of lengths of its other two sides?
+22. There are two walls 2 meters apart, the right wall is moving left by the speed 0.1 m/s, the left wall is moving right by the same speed 0.1 m/s. There is a fly in the middle between the walls, flying by speed 1 m/s. It is flying towards one wall, then when it reaches it it turns around and flies towards the other wall etc. When the walls completely close in, what distance would the fly have traveled? (There is a simple solution.)
+23. Solve these [anagrams](anagram.md): *no cure sir*, *come piss ron*, *ginger*, *nicer shops*, *fog tag*, *trek now*.
+24. At what times, with precision to seconds, do clock hands overlap (just compute AM, PM is the same)?
+25. In 3D computer [graphics](graphics.md) what's the difference between [shading](shading.md) and drawing [shadows](shadow.md)?
+26. Can we say that the traditional feed forward [neural networks](neural_network.md) are [Turing complete](turing_complete.md)? Explain why or why not.
+27. Wicw mx uum yvfe bbt uhmtf ok?
+28. What is the *Big O* time [complexity](complexity.md) of worst case scenario for [binary search](binary_search.md)?
+29. Does the statement "10 does not equal 10" logically [imply](implication.md) that intelligent alien life exists?
+30. What is the principle of [asymmetric cryptography](asymmetric_cryptography.md) and why is it called *asymmetric*?
+31. What is the main reason for [Earth](earth.md) having seasons (summer, winter, ...)?
+32. WARNING: VERY HARD. There are two integers, both greater than 1 and smaller than 100. *P* knows their product, *S* knows their sum. They have this conversation: *P* says: I don't know the numbers. *S* says: I know you don't, I don't know them either. *P* says: now I know them. *S* says: now I know them too. What are the numbers? To solve this you are allowed to use a programming language, pen and paper etc. { Holy shit this took me like a whole day. ~drummyfish }
+33. Did you enjoy this quiz?
 
 ### Answers
 
@@ -151,21 +152,22 @@ Here are some questions to test your LRS related knowledge :D
 15. [GPL](gpl.md), LGPL, AGPL, [MIT](mit.md), BSD, Apache, [CC0](cc0.md), unlicense, zlib, WTFPL, ...; [vim](vim.md), [emacs](emacs.md), [Acme](acme.md), Geany, vi, Notepad++, Neovim, Kate, nano, gedit, ...; [Debian](debian.md), 9front, [OpenBSD](openbsd.md), [FreeDOS](freedos.md), [Haiku](haiku.md), [Minix](minix.md), ReactOS, [GNU](gnu.md)/[Hurd](hurd.md), V6 [Unix](unix.md), FreeRTOS, ...
 16. The number is *N* such that 2^N = 12345678910111213, rounded up, that is ceil(log2(12345678910111213)) = 54.
 17. amplifier, voltmeter, analog hardware for [neural networks](neural_net.md), ...; abacus, mechanical calculators such as Curta, Turing machine made of wood, ...
-18. We can use [cross product](cross_product.md) to find a vector perpendicular to two vectors, so we can take e.g. vectors *U = B - A = {4,3,-2}* and *V = C - A = {0,3,-1}*; their cross product is *UxV = {3,4,12} = n* (just look up the formula for cross product). This is the normal, to normalize it we'll first compute its length, i.e. *|n| = sqrt(3^2 + 4^2 + 12^2) = 13* and then divide each component of *n* by this length, i.e. we finally get *n0 = {3/13,4/13,12/13}*. As a check we can compute [dot product](dot_product.md) of this normal with both *U* and *V* and we should get 0 in both cases (meaning the vectors are perpendicular).
-19. Infinite loop just performs jumps back to some previous program instruction which can be repeated indefinitely, so unless there is something inside the loop that will lead to a crash after many repetitions, an infinite loop will just make the program run forever. With recursion, however, every successive recursive call allocates a new call frame on the call stack (so that the program knows where to return from the function) which will lead to running out of stack memory and to [stack overflow](stack_overflow.md).
-20. no, no, no
-21. The walls will collide in 10 seconds during which the fly has been constantly flying with the speed 1 m/s, so it traveled 10 meters.
-22. *[recursion](recursion.md)*, *[compression](compression.md)*, *[nigger](nigger.md)*, *[censorship](censorship.md)*, *[faggot](faggot.md)*, *[network](network.md)*.
-23. 1:5:27, 2:10:54, 3:16:21, 4:21:49, 5:27:16, 6:32:43, 7:38:10, 8:43:38, 9:49:05, 10:54:32, 12:00:00, you can compute it by making equations for position of the hour and minute hand depending on time, setting them equal and solving, i.e. you get something like *tm / (60 * 12) = (tm / 60) - (tm // 60)* (where *//* is integer division and *tm* is time in minutes); you will find the times are those when minute hand is at multiples of 60 / 11 minues (5:27), i.e. there are 11 such times around the circle and they are evenly spaced.
-24. Shading is the process of computing surface color of 3D objects, typically depending on the object's material and done by GPU programs called [shaders](shader.md); shading involves for example applying textures, normal mapping and mainly lighting -- though it can make pixels lighter and darker, e.g. depending on surface normal, it only applies local models of light, i.e. doesn't compute true shadows cast by other objects. On the other hand computing shadows uses some method that works with the scene as a whole to compute true shadowing of objects by other objects.
-25. We can't really talk about Turing completeness of plain neural networks, they cannot be Turing complete because they just transform fixed length input into fixed length output -- a Turing complete model of computation must be able to operate with arbitrarily large input and output. In theory we can replace any neural network with logic circuit or even just plain lookup table. Significance of neural networks doesn't lie in their computational power but rather in their efficiency, i.e. a relatively small and simple neural network may replace what would otherwise be an enormously large and complicated circuit.
-26. two (or txq); The cipher offsets each letter by its position.
-27. *log2(n)*; Binary search works by splitting the data in half, then moving inside the half which contains the searched item, recursively splitting that one in half again and so on -- for this the algorithm will perform at worst as many steps as how many times we can divide the data in halves which is what base 2 logarithm tells us.
-28. Yes, a false statement implies anything.
-29. The main difference against symmetric cryptography is we have two keys instead of one, one (private) for encrypting and one (public) for decrypting -- neither key can be used for the other task. Therefore encryption and decryption processes differ greatly (while in symmetric cryptography it's essentially the same, using the same key, just in reversed way), the problem looks different in one direction that the other, hence it is called *asymmetric*.
-30. It's not the distance from the Sun (the distance doesn't change that much and it also wouldn't explain why opposite hemispheres have opposite seasons) but the tilted Earth axis -- the tilt changes the maximum height to which the Sun rises above any specific spot and so the angle under which it shines on the that spot; the [cosine](cos.md) of this angle says how much energy the place gets from the Sun (similarly to how we use cosine to determine how much light is reflected off of a surface in [shaders](shader.md)).
-31. 4 and 13, solution: make a table, columns are first integer, rows are second (remember, both *P* and *S* can be making their own table like this too). Cross out whole bottom triangle (symmetric values). *P* doesn't know the numbers, so cross out all combinations of two primes (he would know such numbers as they have only a unique product). *S* knew *P* didn't know the numbers, so the sum also mustn't be a sum of two primes (if the sum could be written as a prime plus prime, *S* couldn't have known that *P* didn't know the numbers, the numbers may have been those two primes and *P* would have known them). This means you can cross out all such numbers -- these are all bottom-left-to-top-right diagonals that go through at least one already crossed out number (combination of primes), as these diagonal have constant sum. Now *P* has a table like this with relatively few numbers left -- if he now leaves in only the numbers that make the product he knows, he'll very likely be left with only one combination of numbers -- there are still many combinations like this, but only the situation when the numbers are set to be 4 and 13 allows *S* to also deduce the numbers after *P* declares he knows the numbers -- this is because *S* knows the combination lies on one specific constant-sum diagonal and 4-13 lie on the only diagonal that in this situation has a unique product within the reduced table. So with some other combinations *P* could deduce the numbers too, but only with 4-13 *S* can finally say he knows them too.
-32. yes
+18. no
+19. We can use [cross product](cross_product.md) to find a vector perpendicular to two vectors, so we can take e.g. vectors *U = B - A = {4,3,-2}* and *V = C - A = {0,3,-1}*; their cross product is *UxV = {3,4,12} = n* (just look up the formula for cross product). This is the normal, to normalize it we'll first compute its length, i.e. *|n| = sqrt(3^2 + 4^2 + 12^2) = 13* and then divide each component of *n* by this length, i.e. we finally get *n0 = {3/13,4/13,12/13}*. As a check we can compute [dot product](dot_product.md) of this normal with both *U* and *V* and we should get 0 in both cases (meaning the vectors are perpendicular).
+20. Infinite loop just performs jumps back to some previous program instruction which can be repeated indefinitely, so unless there is something inside the loop that will lead to a crash after many repetitions, an infinite loop will just make the program run forever. With recursion, however, every successive recursive call allocates a new call frame on the call stack (so that the program knows where to return from the function) which will lead to running out of stack memory and to [stack overflow](stack_overflow.md).
+21. no, no, no
+22. The walls will collide in 10 seconds during which the fly has been constantly flying with the speed 1 m/s, so it traveled 10 meters.
+23. *[recursion](recursion.md)*, *[compression](compression.md)*, *[nigger](nigger.md)*, *[censorship](censorship.md)*, *[faggot](faggot.md)*, *[network](network.md)*.
+24. 1:5:27, 2:10:54, 3:16:21, 4:21:49, 5:27:16, 6:32:43, 7:38:10, 8:43:38, 9:49:05, 10:54:32, 12:00:00, you can compute it by making equations for position of the hour and minute hand depending on time, setting them equal and solving, i.e. you get something like *tm / (60 * 12) = (tm / 60) - (tm // 60)* (where *//* is integer division and *tm* is time in minutes); you will find the times are those when minute hand is at multiples of 60 / 11 minues (5:27), i.e. there are 11 such times around the circle and they are evenly spaced.
+25. Shading is the process of computing surface color of 3D objects, typically depending on the object's material and done by GPU programs called [shaders](shader.md); shading involves for example applying textures, normal mapping and mainly lighting -- though it can make pixels lighter and darker, e.g. depending on surface normal, it only applies local models of light, i.e. doesn't compute true shadows cast by other objects. On the other hand computing shadows uses some method that works with the scene as a whole to compute true shadowing of objects by other objects.
+26. We can't really talk about Turing completeness of plain neural networks, they cannot be Turing complete because they just transform fixed length input into fixed length output -- a Turing complete model of computation must be able to operate with arbitrarily large input and output. In theory we can replace any neural network with logic circuit or even just plain lookup table. Significance of neural networks doesn't lie in their computational power but rather in their efficiency, i.e. a relatively small and simple neural network may replace what would otherwise be an enormously large and complicated circuit.
+27. two (or txq); The cipher offsets each letter by its position.
+28. *log2(n)*; Binary search works by splitting the data in half, then moving inside the half which contains the searched item, recursively splitting that one in half again and so on -- for this the algorithm will perform at worst as many steps as how many times we can divide the data in halves which is what base 2 logarithm tells us.
+29. Yes, a false statement implies anything.
+30. The main difference against symmetric cryptography is we have two keys instead of one, one (private) for encrypting and one (public) for decrypting -- neither key can be used for the other task. Therefore encryption and decryption processes differ greatly (while in symmetric cryptography it's essentially the same, using the same key, just in reversed way), the problem looks different in one direction that the other, hence it is called *asymmetric*.
+31. It's not the distance from the Sun (the distance doesn't change that much and it also wouldn't explain why opposite hemispheres have opposite seasons) but the tilted Earth axis -- the tilt changes the maximum height to which the Sun rises above any specific spot and so the angle under which it shines on the that spot; the [cosine](cos.md) of this angle says how much energy the place gets from the Sun (similarly to how we use cosine to determine how much light is reflected off of a surface in [shaders](shader.md)).
+32. 4 and 13, solution: make a table, columns are first integer, rows are second (remember, both *P* and *S* can be making their own table like this too). Cross out whole bottom triangle (symmetric values). *P* doesn't know the numbers, so cross out all combinations of two primes (he would know such numbers as they have only a unique product). *S* knew *P* didn't know the numbers, so the sum also mustn't be a sum of two primes (if the sum could be written as a prime plus prime, *S* couldn't have known that *P* didn't know the numbers, the numbers may have been those two primes and *P* would have known them). This means you can cross out all such numbers -- these are all bottom-left-to-top-right diagonals that go through at least one already crossed out number (combination of primes), as these diagonal have constant sum. Now *P* has a table like this with relatively few numbers left -- if he now leaves in only the numbers that make the product he knows, he'll very likely be left with only one combination of numbers -- there are still many combinations like this, but only the situation when the numbers are set to be 4 and 13 allows *S* to also deduce the numbers after *P* declares he knows the numbers -- this is because *S* knows the combination lies on one specific constant-sum diagonal and 4-13 lie on the only diagonal that in this situation has a unique product within the reduced table. So with some other combinations *P* could deduce the numbers too, but only with 4-13 *S* can finally say he knows them too.
+33. yes
 
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