What is the smallest number of similar right triangles, with the ratio of their two legs equal to 2:3, that can be fitted together to make a square?
Original printed choices: A) 2; B) 3; C) 4; D) 5; E) 6
Editorial task: give a valid construction and distinguish the source’s stated minimum from what the displayed construction alone proves. The automatic answer is withheld pending a complete suitable lower-bound proof.
Seven examinations have the following candidates:
– Mathematics: An, Bình, Cường and Đạt.
– English: An, Yến, Phương, Giang and Hằng.
– Chemistry: Bình, Yến, Tùng, Dũng and Kiên.
– Literature: Bình, Phương, Lâm and Minh.
– Biology: Giang, Lâm, Nga and Oanh.
– History: Dũng, Minh, Nga and Phong.
– Geography: An, Dũng, Hằng, Kiên, Oanh and Phong.
What is the smallest number of sessions needed so that nobody has two examinations at the same time? Each session may contain one or several examinations.
Isabelle is playing a game with a hexagonal sheet of paper. She rotates the hexagon by the same angle and in the same direction with each move. The illustration shows the sheet at the beginning and after the first move. After how many moves does the sheet look the same as it did at the beginning?
Alex rolls three standard dice and gets a total of 8. All three dice show different numbers. What number is definitely not shown on any of the three dice?
In Kangaroo Town, instead of kilometres the unit used is ‘hops’. Kangaroo Klaus needs 12 minutes to cover one hop. How many hops can he cover in 12 hours?
The picture on the right shows the menu of a burger restaurant. The rain has washed away some of the numbers. The burgers are ordered by price in ascending order, the cheapest being the "veggie" burger. What is the smallest possible price of the "deluxe" burger?
Five circles, each of area $8\,\mathrm{cm}^2$, overlap as shown. Each overlapping section has area $1\,\mathrm{cm}^2$. What is the total area of the figure in $\mathrm{cm}^2$?
If Paul sets the number 0000 on his bicycle lock, he sees 8888 at the point marked with an x. To open the lock, he must turn the rings so that the number 2815 is at the x mark. What number is then next to the arrows?
A mouse wants to get to a piece of cheese. From each square it can only move to the square to the right of it or directly below it. How many different paths lead the mouse to a piece of cheese?
In a 60 m hurdles race, there are 5 hurdles. The first hurdle is 12 m after the start. The distance between any two consecutive hurdles is 8 m. How far is the last hurdle from the finish line?
Emma wants to write a number in each circle (see diagram). She wants each number to be equal to the sum of the numbers in the two adjacent circles. She has already written two numbers. Which number will she write in the grey circle?
Sanja has two bowls containing numbered balls. In the left bowl, there are seven balls with the numbers 1, 2, 6, 7, 10, 11 and 12. Their arithmetic mean is 7.0. In the right bowl there are five balls with the numbers 3, 4, 5, 8 and 9; their arithmetic mean is 5.8. Sanja wants to increase the arithmetic mean of the numbers in both bowls. Which ball must she transfer from the left bowl to the right to do this?
Theo is standing on a treadmill in the gym. He sees two stopwatches. The left one shows the time that has elapsed since he started his workout. The right one shows the time remaining until the end of his workout. At some point both stopwatches will display the same time. What will they display at that point?
