Combinatorics - practice for 10 year olds
Number of problems found: 19
- Paths to the hill
From a car park it is possible to ascend to the top of a hill on three different hiking trails or by going up by cable car, and in the same four ways it is possible to descend from the hill back to the car park, as illustrated in the picture. By a path to - Chess competition
Four chess players took part in the competition. How many matches would have taken place if every chess player had played with everyone just once? - Three-digit number creation
How many different three-digit numbers divisible by five can we create from the digits 2, 4, and 5? The numerals can be repeated in the created number. - Customer 5
A customer decided to buy a Laura bed with a wooden slatted frame (available in 2 types) and an extra-firm mattress (available in 4 types) in one of three colours. Determine how many different combinations of the Laura bed with a wooden slatted frame and - Pair combinations
From 5 girls and four boys, we have to choose one pair, boy and girl. List all the pairs in which the individual boys will be. Attention, these are four examples. How many pairs are there? - Digits
How many odd four-digit numbers can we create from digits 0, 3, 5, 6, and 7? (a) the figures may be repeated (b) the digits may not be repeated - Anti-birthdays
Štefka likes to celebrate, so apart from her birthday she came up with anti-birthdays as well: the date of anti-birthdays arises so that the number of the day and the number of the month in the date of birth are swapped. She herself was born on 8.11., so - Twins with friend
Twins Dana and Jane went to the cinema with their friend Betty. Only six seats in the second row were available in the cinema. The twins want to sit next to each other. Dana always sits to the right of Jane, and Betty sits next to one of them. In how many - Three-digit numbers
How many different three-digit natural numbers can be created so that the digits are different and the last digit is 0? - Mr. Michal
Mr. Michal commutes to work and back on the motorway. Sometimes he is in a hurry and exceeds the permitted speed, at other times he follows the rules. Sometimes on the motorway the speed is checked by radar, and at other times not. a) how many different c - Wardrobe code Lucia has a lock on her wardrobe that opens with a 4-digit code (such as 0000, 0089, or 9123). Lucia forgot her code. But she knows that the sum of all four digits of her code is 4. How many such codes are there?
- Four-digit eight count How many four-digit numbers are there in which there are at least three eights
- Family visit count
Dulikovci, Elikovci, Filikovci, and Galikovci visited each other often last month. Each family visited each family exactly once. How many visits did all four families make together? If two families came to visit one family simultaneously, count it twice. - Classmate seating arrangements
Classmates Annie, Bea, Ella, and Dana can sit next to each other on the bus. What and how many ways can they sit down? - Dice Rolls for Sum
Stella rolls a standard six-sided die. How many times does she have to roll the die to be sure that the sum of the results will be at least 4? - Train colors
The locomotive pulls six wagons. Each of the wagons is either red or blue. The order of colors of individual wagons is the same from the front and back. How many such trains can you draw? - Digits
Write the smallest and largest 2-digit natural number. - Testing 5
Viktória has many T-shirts - 3 white, 1 yellow, 3 blue, 2 green, 4 pink, 1 black, 2 orange. Which of the following statements is true? A: It is equally probable that Viktória will put on a white T-shirt as a pink T-shirt. B: It is more probable that Viktó - 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.
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