Equation + Mathematical Olympiad - practice problems - last page
Number of problems found: 52
- Coefficients 4445
Find all triplets P (x) = a * x² + b * x + c with the integer coefficients a, b, and c to which it applies P (1) - Cakes Z8-I-5
Mom brought ten cakes of three types: coconut was less than Meringue Cookies, and most were caramel cubes. John chose two different kinds of cakes. Stephan did the same and for Margerith left only the cakes of the same type. How many coconut, Meringue Coo - Star equation
Write digits instead of stars so that the sum of the written digits is odd and is true equality: 42 · ∗8 = 2 ∗∗∗ - MO-Z5-3-66 tiles
The picture shows square tiles with a side of 10 dm, composed of four identical small rectangles and squares. The circumference of a small square is five times smaller than the circumference of the entire tile. Determine the dimensions of the rectangle.
- Three friends
Three friend squirrels together went to collect hazelnuts. Zrzecka found more than twice Pizizubka, and Ouska was even three times more than Pizizubka. On the way home, they talked while eating and were cracking her nuts. Pizizubka ate half of all nuts co - MO SK/CZ Z9–I–3
John had the ball that rolled into the pool and swam in the water. Its highest point was 2 cm above the surface. The diameter of the circle that marked the water level on the ball's surface was 8 cm. Find the diameter of John's ball. - Z9-I-4
Kate thought of a five-digit integer. She wrote the sum of this number and its half in the first line of the workbook. On the second line, write a total of this number, and its one fifth. She wrote a sum of this number and its one nines on the third row. - Soup
On Monday, we cook 25 pots and ten boilers of soup. On Tuesday, 15 pots and 13 boilers. On Wednesday, 20 pots and on Thursday, 30 boilers. On Monday and Tuesday was cooked the same amount of soup was. How many times is more soup cooked on Thursday than on - Chamber
In the chamber, light is broken, and all from it must be taken at random. Socks have four different colors. If you want to be sure of pulling at least two white socks, we have to bring them out 28 from the chamber. To have such certainty for the pair of g
- Exchanged 2214
In the table, the exchange rate list is an exchange office, but question marks replace some values. The exchange office exchanges money at the rates quoted and does not charge any other fees. nákup prodej 1 EUR 26,20 CZK 28,00 CZK 1 GBP b=? CZK c=? CZK 1. - Square grid
A square grid consists of a square with sides of a length of 1 cm. Draw at least three patterns, each with an area of 6 cm² and a circumference of 12 cm, and their sides in a square grid. - Pytagoriade
Two fifth-graders teams compete in math competitions - Mathematical Olympiad and Pytagoriade. Of the 33 students who competed in at least one of the contests, 22 students. Students who competed only in Pytagoriade were twice as many who just competed in t
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