Pythagoras contest - practice problems - page 2 of 3
Direction: Solve each problem carefully and show your solution in each item.Number of problems found: 47
- All pairs
Find all pairs (m, n) of natural numbers for which is true: m s (n) = n s (m) = 70, where s(a) denotes the digit sum of the natural number a. - Census pyramid
Vojta added five different prime numbers to the top row of the census pyramid. Their sum was 50. What was the biggest number he could get "down"? - Candles
Before Christmas, Eva bought two cylindrical candles—red and green. Red was 1 cm longer than green. She lit a red candle on Christmas Day at 5:30 PM and a green candle at 7:00 PM, leaving them on fire until they burned. At 9:30 PM, both candles were the s - Yesterday 13711
If the day before yesterday was the day of the week, what day of the week would it be from today in 50 days? (0 = Monday, 6 = Sunday)
- Apples and pears
Apples cost 50 cents a piece, pears 60 cents a piece, bananas cheaper than pears. Grandma bought five pieces of fruit. There was only one banana, and I paid 2 euros 75 cents. How many apples and how many pears? - 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 - Special watch
Fero 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? - Solutions 5453
Tongue twister. Replace the letters with numbers to get the correct sum: ŠKRZ KRK STRČ ______ PRST How many solutions does the task 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 much has the task of solutions?
- 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. - Five-crowns 4879
Eva 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? - 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 4378
Find out the other three members of the sequence and write their sum: 1,29,2,28,3,27, - Entrepreneur 4367
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
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. JDo you have homework that you need help solving? Ask a question, and we will try to solve it. Solving math problems.
