Prime numbers - practice for 14 year olds - last page
Number of problems found: 99
- Parachutists
During freefall, parachutists were first held in groups of 4, then 6, then 9, 12, and finally 18 members. How many parachutists jump at least should be, if at each group must all be involved. - Nuts
How many must we have at least nuts if we can equally divide it to 10 children, 12 children, or 15 children and any nuts left? - Combinations
How many different combinations of two-digit number divisible by four arises from the digits 3, 5, and 7? - Sports games
Pupils of the same school participated in district sports games. When dividing into teams found that in the case of the creative teams with four pupils remaining one pupil, in the case of five-member teams with remaining two pupils, and in the case of six
- Unknown number
An unknown number is divisible by exactly three different primes. When we compare these primes in ascending order, the following applies: • Difference between the first and second prime numbers is half the difference between the third and second prime num - Snowman 2
On the medal, which has the shape of a circle with a diameter 18 cm, is sketched a snowman so that the following requirements are met: 1. snowman is composed of three circles, 2. space over the snowman is the same as under it, 3. diameters of all circles - Racing track
On the racing track circling three cars. The first pass one circuit for 8 seconds, the second for 20 seconds, and a third for 8 seconds. a) Calculate the number of seconds since starting to catch all three cars together for the first time again across the - Snowman
In a circle with a diameter of 40 cm are drawn three circles (as a snowman) where: its diameters are integers, each larger circle diameter is 2 cm larger than the diameter of the previous circle. Determine snowman height if we wish for the highest snowman - Sugar - cuboid
Pablo received from his master a cuboid composed of identical sugar cubes with a count between 1000 and 2000. The Pejko eat sugar cubes in layers. On the first day, eat one layer from the front. On the second day, one layer from the right, and on the thir
- Divisors
The sum of all divisors unknown odd number is 2112. Determine the sum of all divisors of a number that is twice unknown numbers. - Segments
Line segments 69 cm and 3.7 dm long we divide into equal parts which lengths in centimeters is expressed integer. How many ways can we divide? - Package
The package has no more than 66 m of cloth. If we just cut it all on the blouses or all on dresses, no cloth left to remain. On the one blouse consumes 1.3 m of cloth and on one dress 5 m. Determine the amount of the cloth in the package. - TV commercials
For the typical one-hour prime-time television slot, the number of minutes of commercials is 3/8 of the actual program's minutes. Determine how many minutes of the program are shown in that one hour. - Divisibility
Determine the smallest integer which divided 11 gives remainder 4. When divided, 15 gives remainder 10 and when divided by 19 gives remainder 16.
- Numbers
Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17. What is its sum? - Diofant 2
Is equation 70x +52y = 34 solvable on the set of integers Z? - Diofant equation
In the set of integers (Z), solve the equation: 212x +316y =0 Write result with integer parameter t in Z (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions) - Rectangles
How many rectangles with area 3152 cm² whose sides are natural numbers? - Seedcake
Seedcake costs 44 cents. How many minimum seedcakes must we buy that we can pay in cash, only whole euros?
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