Mathematical Olympiad - practice for 11 year olds
Number of problems found: 37
- Characters 82998
Adam wrote the following sum with five secret adders: a + bb + ccc + dddd + eeeee. He revealed that the characters "a, b, c, d, e" represent the different digits 1, 2, 3, 4, and 5 and that the resulting sum is divisible by 11. Which is the smallest and wh - Determine 82724
A right triangle has an area of 36 cm². A square is placed in it so that two sides of the square are parts of two sides of a triangle, and one vertex of the square is in a third of the longest side. Determine the content of this square. - Originally 80757
There were 45 sheep and several shepherds in the meadow. After half of the shepherds and a third of the sheep left the meadow, the remaining shepherds and sheep had a total of 126 legs. All sheep and all shepherds usually had leg counts. how many shepherd - Characteristics 65294
Kuba wrote down a four-digit number, two evens, and two odds. If he crossed out both even digits in that number, he would get a number four times smaller than if he crossed out both odd digits in the same number. What is the most significant number with t
- Shepherd
Kuba makes a deal with a shepherd to take care of his sheep. Shepherd said to Kuba that he would receive twenty gold coins and one sheep after a year of service. But Kuba resigned just after the seventh month of service. But the shepherd rewarded him and - The king
The king divided ducats among his sons. He gave the eldest son a certain number of ducats, gave the younger one ducat less, gave the other one ducat less, and proceeded to the youngest. Then he returned to his eldest son, gave him one ducat less than a wh - Restriction 7442
The figure shows two rows of hexagonal boxes that continue to the right without restriction. Fill in one field with one positive integer so that the product of the numbers in any three adjacent fields is 2018. Determine the number that will be in the top - -------------- 7311
In the following addition example, the same letters represent the same digits, and the different letters represent different digits: RATAM RAD -------------- ULOHY Replace the letters with numbers so that the example is correct. Find two different replace - Quadrilaterals 7224
In the ABCDEFGHIJKL, the two adjacent sides are perpendicular to each other, and all sides except the AL and GF sides are identical. The AL and GF parties are twice as long as the other parties. The lines BG and EL intersect at point M and divide the dode
- Ticháček 7185
Mr. Ticháček had three gypsum dwarfs in the garden: the largest was called Maško, the middle Jarko, and the smallest Franko. Since he liked to play with them, he found out that when he puts Fan on Jarek, they are as tall as Maško. On the other hand, when - Definitely 7179
Ivan and Mirka shared pears in the mission. Ivan always takes two pears, and Mirka takes half of what remains in the mission. Thus, Ivan, Mirka, Ivan, Mirka, and finally Ivan, who took the last two pears, took them away. Definitely. Who had more pears, in - Clubhouse
There were only chairs and tables in the clubhouse. Each chair had four legs, and the table was triple. Scouts came to the clubhouse. Everyone sat on their chair, two chairs were left unoccupied, and the number of legs in the room was 101. How many chairs - Kilometers 6417
It is 16 km from point A to B. from point C to B, it is 20 km from point C to D, it is 19 km how many kilometers is it from point D to point A - Remaining 5534
On the table lay eight cards with the numbers 2,3,5,7,11,13,17,19. Fero chose three cards. He added the numbers written on them and found that their sum was 1 more than the sum of the numbers on the remaining cards. Which cards could have been left on the
- Originally 5427
There were red and green candies in the tin. Čenek ate 2/5 of all the red candies, and Zuzka ate 3/5 of all the green candies. Now, the red candies make up 3/8 of all the candies in the can. How many candies were originally in the can? - Double-digit 5411
Anička and Blanka each wrote one double-digit number, which started with a seven. The girls chose different numbers. Then each inserted a zero between the two digits, giving them a three-digit number. Everyone subtracted their original two-digit number fr - Something 5385
Janko got pocket money and wants to buy something good for it. If he purchased four cakes, it would increase by 0.50 euros. If he wanted to buy five cakes, he would miss 0.60 euros. He would spend all his pockets on the rest if he bought two cakes and thr - 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. - 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.
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Mathematical Olympiad - practice problems. Maths practice for 11-year-olds..