The Clearly Impossible Puzzle 200 Piece! - Medium - Very Difficult and Fun! - Clear Acrylic

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Let us call the split of a number A into two terms A=B+C a 2-split. There is no need for any advanced knowledge like Goldbach's conjecture or the fact that for the product B·C of such a 2-split to be unique (i.e. there are no other two numbers that also when multiplied yield the same result). But with Goldbach's conjecture, along with the fact that P would immediately know X and Y if their product were a semiprime, it can be deduced that the sum x+y cannot be even, since every even number can be written as the sum of two prime numbers. The product of those two numbers would then be a semiprime. On the other hand, when the limit is X + Y ≤ 1685 or higher, there appears a second solution X = 4, Y = 61. Thus, from then on, the problem is not solvable in the sense that there is no longer a unique solution. Similarly, if X + Y ≤ 1970 or higher a third solution appears ( X = 16, Y = 73). All of these three solutions contain one prime number. The first solution with no prime number is the fourth which appears at X + Y ≤ 2522 or higher with values X = 16 = 2·2·2·2 and Y = 111 = 3·37. If Prada can figure out the numbers from the first statement, then the product must be unique among the remaining possible sums. For example, if the product were 30, Prada would be unable to figure out the numbers because the sum could be 11 = 5 + 6 or 17 = 2 + 15. So for each of the remaining sums, we write out the possible products: Considering the new information in Table 2, Pete once again looks at his product. The sums of all of the possible 2-splits of his product except one have disappeared from Table 2 compared to all numbers between 5 and 100 that were considered as sums from the outset. The only one that remains must be the sum of the two hidden numbers X and Y whose product X·Y he knows. From the sum and the product, it is easy to know the individual numbers and thus he tells Sue that "Now I know X and Y". Pete is now done and exits the game. If Prada had a product with only one possible factorization (e.g., 15 = 3 * 5), Prada would know the numbers right away. So if Sam knows that Prada cannot know the numbers with just the product, then the sum is such that no combination of addends is the sole factorization of the product.

Inspired by the spectacular geode, this beautiful yet impossible puzzle comes in complex jigsaw pieces to challenge you. The puzzle recreates the intricate crystalline pattern of geode and is cut into 180 unusual pieces that makes it fiendishly difficult. So now you know how a beautiful devil looks like 5. The Lines Puzzle by Bgraamiens Puzzles The reader can then deduce the only possible solution based on the fact that S was able to determine it. Note that for instance, if S had been told 97 (48 + 49) and P was told 2352 (48 * 49), P would be able to deduce the only possible solution, but S would not, as 44 & 53 would still be a logically possible alternative. Darus, Alex (April 24, 2020). "Here are 10 online games from your childhood that you can still play". Alternative Press. Archived from the original on June 28, 2022 . Retrieved August 21, 2023.

The Impossible Quiz

Because none of these products has a unique factorization (i.e., none of these are the product of two prime numbers), Sam knows Prada cannot know the solution yet – hence the first statement. a b c d White, Billy (December 23, 2017). "Celebrating With The Impossible Quizmas". Game Industry News. Archived from the original on February 23, 2018 . Retrieved August 21, 2023. The problem can be generalized. [2] The bound X + Y ≤ 100 is chosen rather deliberately. If the limit of X + Y is altered, the number of solutions may change. For X + Y< 62, there is no solution. This might seem counter-intuitive at first since the solution X = 4, Y = 13 fits within the boundary. But by the exclusion of products with factors that sum to numbers between these boundaries, there are no longer multiple ways of factoring all non-solutions, leading to the information yielding no solution at all to the problem. For example, if X = 2, Y = 62, X + Y = 64, X· Y=124 is not considered, then there remains only one product of 124, viz. 4·31, yielding a sum of 35. Then 35 is eliminated when S declares that P cannot know the factors of the product, which it would not have been if the sum of 64 was allowed. The Impossible Quiz™ Now Available Free-to-Play - Only on Android™!" (Press release). Business Wire. November 17, 2011 . Retrieved August 21, 2023.

Now this puzzle on the list is out of the world. No, literally — we’re talking about the Infinite Galaxy Puzzle. Based on the photo of stars being born in the Carina Nebula taken from the Hubble Space Telescope, this puzzle is a total feast to the eyes when fully assembled. But beware, it’s going to be as tiring as an intergalactic mission. Seriously, we’re talking about an amorphous and formless galaxy, no specific starting point, intricate colour gradient, infinite combinations, and unusual puzzle pieces. But this impossible puzzle is a guaranteed mental stimulation. 7. Vintage Map of London You’ll Get Lost In This means x and y cannot both be prime numbers, and the sum Sam was provided has no combination of addends that are both prime. For example, we can eliminate 9 because it can be formed by 2 + 7 which are prime, so Sam would be unable to conclude that Prada cannot deduce the numbers.This section does not cite any sources. Please help improve this section by adding citations to reliable sources. Unsourced material may be challenged and removed. ( August 2018) ( Learn how and when to remove this template message) Friedman, Lex (March 15, 2010). "iPhone quiz apps". Macworld. Archived from the original on August 26, 2023 . Retrieved November 12, 2023.

If you're not phased so far and think you have what it takes to conquer the impossible, put your knowledge, logic, and problem-solving skills where your mouth is in this one-of-a-kind puzzler by Splapp-me-do. Each level will challenge you with a series of devious and downright ridiculous questions, each with four possible answers, each more ridiculous than the last. And beware: the answers are often misleading or humorous, so it's up to you to use your critical thinking skills to determine the correct response. Sam was provided x + y = 17, and can list out the possible products that Prada could have been provided: After the first statement, Prada can eliminate one of these possibilities. If Sam was provided 28, one of the possible products would have been 115 = 5 * 23, which is a unique factorization, meaning Sam would be unable to confidently make the first statement. So Prada knows Sam must have been provided 17, and now knows x and y. If the condition Y> X> 1 is changed to Y> X> 2, there is a unique solution for thresholds X + Y ≤ t for 124 < t< 5045, after which there are multiple solutions. At 124 and below, there are no solutions. It is not surprising that the threshold for a solution has gone up. Intuitively, the problem space got "sparser" when the prime number 2 is no longer available as the factor X, creating fewer possible products X·Y from a given sum A. When there are many solutions, that is, for higher t, some solutions coincide with those for the original problem with Y> X> 1, for example X = 16, Y = 163.So P now knows the numbers are 4 and 13 and tells S that he knows the numbers. From this, S now knows that of the possible pairs based on the sum (viz. 2+15, 3+14, 4+13, 5+12, 6+11, 7+10, 8+9) only one has a product that would allow P to deduce the answer, that being 4 + 13.

Then we eliminate the products that are common between these sums. When this is done, we observe that 17 has only one remaining product (52) and the others all have more than one. Therefore the sum is 17 and the product is 52, so the numbers are 4 and 13! Sue and Otto recalculate Table 1, this time only counting products of 2-splits from sums that are in Table 2 instead of from all numbers in the range 5 to 100 as in the original Table 1. This updated table is called Table 1B. Sue looks at all the products of the 2-splits of her sum and finds that only one of them appears exactly once in Table 1B. This must then be the product Pete has, and she can infer the two numbers from their sum and product as easily as Pete did. Thus, she tells Otto (Pete is already gone) that "Now I also know X and Y". Sue is now also done and exits the game, only Otto remains. Answer 84: You need to touch only the shooting star while avoiding the meteors. But before that, you must first collect the “Skips” that are floating around because you will need them later on. (the good thing is that it can be skipped. It’d be “impossible” if it weren’t skippable.) Overall, The Impossible Quiz is a fun and challenging game that offers a unique and engaging puzzle experience for players looking for a challenge.

a b c d e f g h i j Chan, Harri (August 1, 2022). "The Impossible Quiz made me rage quit — and learn to collaborate". Polygon. Archived from the original on August 1, 2022 . Retrieved August 21, 2023. If the condition X + Y ≤ t for some threshold t is exchanged for X·Y ≤ u instead, the problem changes appearance. It becomes easier to solve with less calculations required. A reasonable value for u could be u = t· t/4 for the corresponding t based on the largest product of two factors whose sum are t being ( t/2)·( t/2). Now the problem has a unique solution in the ranges 47 < t< 60, 71 < t< 80, 107 < t< 128, and 131 < t< 144 and no solution below that threshold. The results for the alternative formulation do not coincide with those of the original formulation, neither in number of solutions, nor in content.