Equation + Pythagoras contest - practice problems
Number of problems found: 16
- Two-digit 82521
Karel had to multiply two two-digit numbers. Out of care, he changed the order of the digits in one of the factors and got a product that was 4,248 less than the correct result. What is the correct result? How much should Karl have earned? - Position 81987
Find a number with six digits. If you put the last digit before the first, you get a new number that is five times larger. The digits between must not change their position. - Determine 80714
Three different numbers are given. The average of the average of two smaller numbers and the average of the two larger numbers is equal to the average of all three numbers. The average of the smallest and largest number is 2022. Determine the sum of the t - Nightmares 80568
At the dream market, she offered the Sphinx to a traveler for four dreams, seven illusions, two naps, and one nightmare. Another has seven dreams, four illusions, four naps, and two nightmares. The Sphinx always measures the same for all travelers. How ma - Beginning 66104
The kangaroo always jumps three steps up. Each time he jumps, the bunny jumps down two steps. On which stairs will they meet? The kangaroo stands on the 1st step at the beginning and the bunny on the 100th. - Four-digit 55481
Find all four-digit abcd numbers to which: abcd = 20. ab + 16. cd, where ab and cd are double digits numbers from digits a, b, c, and d. - 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? - 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 - 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? - Equation algebraogram
Solve the equation: oco + ivo = cita How much has the task of solutions? - 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 Kč. The Blue bike costs 3600Kč and the red bicycle 3200Kč. - King's birthday
To celebrate the king's birthday, workers fire 1/5 all purchased rockets. To celebrate the Queen's birthday, fire 1/6 of the remaining rockets, and to celebrate the birthday of the king's son, the remaining 15,000 rockets. How many rockets did they purcha - Everyone 3299
The three brothers had 24 apples. Everyone kept half and divided half between the two brothers. Everyone had as many apples as they had three years ago. How old were they? - Short cut
Imagine that you are going to a friend. That path has a length 120 meters. Then turn doprava and go other 630 meters, and you are at a friend's. The question is, how much will the journey be shorter if you go direct across the field?
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