by Today I used to give you the following two problems. Here you are back with solutions.
1. Tricky triangle
What is the length of the display, the dashed line?
Solution: x = 1
The reason why most people do not solve this is that the triangle is degenerate: it is actually a line, not a triangle.
The horizontal side has length 8. The other two sides add 8, so that these two sides are on the top of the horizontal line.
People who find that the triangle is degenerate still misunderstood the riddle because they immediately assume that the distance between A and D 0 is. A moment is reflected and they realize that it is 1.
2. Rockin ‘rectangle
It is light enough to divide a square into five rectangles.
But can you:
i) Share a square into five rectangles, so that no two rectangles have a whole side together – that is, the pages on adjacent rectangles never begin And End the same points? (The rectangles don’t have to have the same size or shape.)
ii) Do you share an 11 x 11 square into five rectangles so that the ten side lengths are the total numbers of 1 to 10? Tip: If you have solved part I, use this arrangement of rectangles.
Solution
i) You can change the size of the rectangles and turn around the side to go in the other direction, but this is the only pattern that works.
II) There are two solutions, both have a core of 4×7. You will get there through experiments and errors and observe the restrictions. The side length is 11, so there must be four sets of two side lengths that add up to 11. The area is 121, so that the sum of the areas of the 5 rectangles add up to 121. In other words, how can you divide the numbers from 1 to 10 into couples, the sum of which is 121?
I hope you enjoyed these puzzles, I’ll be back in two weeks.
I have set a mystery here on alternative Mondays since 2015. I am always looking for great puzzles. If you want to suggest one, send me an e -mail.
