Reason - practice for 13 year olds - page 17 of 41
Number of problems found: 810
- Letters
ABC + DEF = GHIJ replace letters with numbers so that the sum is correct (different letters = different numbers) - Chocolates
How many ways can we distribute eight different chocolates to four children? - Children 7350
Mom sent half of her children and half a child shopping. Only one of her children remained at home. How many children does my mother have? - Particular 7338
Two workshops of a particular company produced 25 parts a day. To have 300 pieces, one worked for ten days and the other for 15 days. How many parts did each workshop make per day?
- Three-digit numbers
Use the number 4,5,8,9 to write all three-digit numbers without repetition. How many such numbers are there? - Odd/even number
Pick any number. If that number is even, divide it by 2. If it's odd, multiply it by three and add one. Now, repeat the process with your new number. If you keep going, you'll eventually end up at one every time. Prove. - Single-digit 7302
Four different digits were on the four cards, one of which was zero. Vojta composed the largest four-digit number from the cards, and Martin the smallest four-digit number. Adam wrote the difference between Vojtov's and Martin's numbers on the board. Then - Harvesters
The first harvester will harvest the grain from the field in 20 hours, and the second, the more powerful in 10 hours. How long will it take to harvest this field by both harvesters if the second harvester has to be set up first, which takes 2 hours? The f - Compartments 7275
Tomáš has two compartments with CD-ROMs. The arithmetic average of the number of CDs in both bins is 30. If he added 10 more CDs to the first bin, there would be 1.5 times more CDs than in the second bin. How many CDs are in each compartment?
- Mathematics 7270
Mišo has also been preparing for testing 9 for a long time. He devotes a third of his time to Czech, half of his time to mathematics, and discusses with his father for 10 minutes. How many minutes a day does Mišo prepare? - Craftsman 7263
To make a ladder, the craftsman needs to cut as many rungs of the same length as possible. He is to cut them from two boards, one is 220cm long, and the other is 308cm long. How long will the bars be, and how many will there be? - Hundred 7239
Each of the six horses ate just 75 days in a hundred days. How many and at least days could be during which at least five horses ate? - Younger 7202
If Nina were nine times older and her mother was nine times younger, they would be 85 years old. So, Ninka is 85, and Mom is 85. - Game 27
Susan wanted to play the game. In the beginning, the first says a number from 1 to 8. Then the second player adds a number from 1 to 5 and tells the sum. Again, Susan adds a number from 1-5 and says sum, etc. The winner must say the number 27. What first
- Minutes 7177
The tank holds 140 liters of water. The tank is filled with a tap in 5 minutes, and the drain is emptied in 7 minutes. How long will it take for the empty tank to fill if we open the faucet and drain? - Languages 7160
Out of 100 students, 30 studied German, 28 studied German, 42 learned French, eight studied German and German, 10 German and German, and 5 German and German. How many students have learned all three languages? - Filip's 7158
Filip's friend is three times younger than Filip's father. He will be two years younger. How old is Filip's friend? - Circumference 7143
Peter drew a regular hexagon, the vertices of which lay on a circle 16 cm long. Then, for each vertex of this hexagon, he drew a circle centered on that vertex that ran through its two adjacent vertices. The unit was created as in the picture. Find the ci - Mathematical 7136
Out of 50 pupils, 44 solved at least one of the Olympiads - MO Mathematical Olympiad and BO Biology Olympiad. Twenty pupils still need to solve the MO. Of those who dealt with both Olympiads, 1/3 of those who dealt with just one were. How many pupils solv
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