Pythagoras contest - practice problems - page 3 of 4
Remember: Solve each problem thoughtfully and make sure to show your complete solution for every question.Number of problems found: 67
- Two cars on ring
Two cars were on the round track (ring) in the adjacent tracks, the first on the inner track and the second on the outer track. Both cars started at the same time from one starting track. The first toy car drove four laps simultaneously, and the second to - Self-counting machine
The self-counting machine works exactly like a calculator. The innkeeper wanted to add several three-digit natural numbers on his own. On the first attempt, he got the result in 2224. To check, he added these numbers again, and he got 2198. Therefore, he - Equilateral triangle ABC
In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near point C, and point M lies on one-third of the side of the AC side closer to point A. Find what part of the ABC triangle contains the triangl - Triangulum
Student Ernest paints colorful lines and points. In his notebook, he had two drawings. In the drawing called Triangulum, there were 3 colored lines. The points where the lines intersected were highlighted with black dots. In the second drawing, he had 4 l - Special watch
Frank bought a special watch on the market. It has only one (minute) hand and a display showing the angle between the hour and minute hands. How many hours was his watch shown? The minute hand points to number 2; the display shows 125°. - Two rectangles
I cut out two rectangles with 54 cm² and 90 cm². Their sides are expressed in whole centimeters. If I put these rectangles together, I get a rectangle with an area of 144 cm². What dimensions can this large rectangle have? Write all options. Explain your - Triplets
Three years ago, the triplets Pavel, Petr, Luke, and their five-year-old sister Jane had been together for 25 years. How old is Jane today? - They held
A 100-metre race was held at school. Peter, Jan, Andrej, Radko, and Miro advanced to the final. Peter finished either second, third, or fourth. Jan was not the winner. Andrej finished one place behind Jan. Radko did not finish in second place. Miro finish - Letter puzzle
Cryptarithmetic puzzle. Replace the letters with digits to get the correct sum: ŠKRZ KRK STRČ ______ PRST How many solutions does the problem have? - One million
Write the million number (1000000) using only nine numbers and algebraic operations plus, minus, times, divided, powers, and squares. Find at least three different solutions. - Equation algebraogram
Solve the equation: oco + ivo = cita How many solutions does the problem have? - Alarm clock
The old watchmaker has a unique digital alarm in its collection that rings whenever the sum of the alarm's digits equals 21. Find out when the alarm clock will ring. What is their number? List all options. - Coin count
Eve had seven coins. Crowns, two-crowns, and five-crowns. At least two of each. How many did she have if she could buy three packs of gum for six crowns? - Chocolate 6
An international gang of chocolate smugglers led by the famous Jack Crooked Nose, who has 7 collaborators, singled out the Bratislava airport as a crossroads for their business. An aircraft from Bratislava to Stockholm flies every third day. An aircraft f - Shuttle transport
A river 777 km long flows through forests and meadows, and here and there a port flickers on its bank. Between 2 of 5 ports on the river, there is a permanent shuttle transport. It is provided by the 77-year-old ship Quendolína with captain Bluebeard, who - Bicycles
You're the owner of the transport's learning playground. Buy bicycles of two colors, but you've got to spend accurately 120000 CZK. The Blue bike costs 3600 CZK and the red bicycle 3200 CZK. - Sequence members
Find out the other three members of the sequence and write their sum: 1,29,2,28,3,27, - Cube painting
Entrepreneur Kostkoš wanted to produce colorful blocks for schools. But he gave them to another businessman to paint, who asked €1,117.2 for painting 1,000 cubes. The area that needs to be painted on one cube is 294 square centimeters. Please write how ma - Take a photo
Four boys live in a three-story house. Each lives on a different floor. We know the following about them: - Josef is a philatelist. - Viktor does not live on the top floor and is not a photographer. - Ivan is friends with an amateur photographer who lives - David number
Jane and David train in the addition of decimal numbers so that each of them will write a single number, and these two numbers will then be added up. The last example was 11.11. David's number also had the same number of digits before and after a point. J
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