Pythagoras contest - practice for 12 year olds
Number of problems found: 14
- Sequence 4378
Find out the other three members of the sequence and write their sum: 1,29,2,28,3,27, - 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. - 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 - Grandma
Grandma is 57 years older than her two twin granddaughters. If we add the ages of an older woman with both granddaughters, we get the number 99. How old is her old woman? - Different 55491
Add the same numbers after the same letters and different numbers after the other letters so that equality applies: KRAVA + KRAVA = MLIEKO, where K is an odd digit. - Classroom 81621
On a classroom clock, the large (minute) hand on the clock will travel through an angle of 120 degrees in some time. What angle does the small (hour) hand pass in this time? - Different 82683
There are candies from 1 to 10 in ten different packages. Each child took two packages. They got so many candies: Anka: 5 Zuzka: 7 Katka: 9 Monica: 15 How many candies does Lucka have? - 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? - Phone number
Ivan's phone number ends with a four-digit number: When we subtract the first from the fourth digit of this four-digit number, we get the same number as when we subtract the second from the third digit. If we write the four-digit number from the back and - 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. - David number
Jane and David train the addition of the decimal numbers so that each of them will write a single number, and these two numbers then add up. The last example was 11.11. David's number also had the same number of digits before and after a point. Jane's num - 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. - 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 - 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
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