Diofant 2

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1. Diofant equation
   In the set of integers (Z) solve the equation: ? Write result with integer parameter ? (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions)
2. Legs
   In the room are four-legged chairs, three-legged stool, and all are sitted with (one) people. I counted all the leg room and there were a total of 39. How many are there chairs, stool and people?
3. One hundred stamps
   A hundred letter stamps cost a hundred crowns. Its costs are four levels - twenty tenths , one crown, two-crown and five-crown. How many are each type of stamps? How many does the problem have solutions?
4. Red and white
   Simona picked 63 tulips in the garden and tied bicolor bouquets for her girlfriends. The tulips were only red and white. She put as many tulips in each bouquet, three of which were always red. How much could Simon tear off white tulips? Write all the optio
5. Two unknown numbers
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6. Balls
   Michal said to Martin: give me one ball and I'll have twice as you. Martin said: give me 4 and we will have equally. How many balls each have?
7. Gauss
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8. Sum of two primes
   Christian Goldbach, a mathematician, found out that every even number greater than 2 can be expressed as a sum of two prime numbers. Write or express 2018 as a sum of two prime numbers.
9. Tissues
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10. Toy cars
    Pavel has a collection of toy cars. He wanted to regroup them. But in the division of three, four, six, and eight, he was always one left. Only when he formed groups of seven, he divided everyone. How many toy cars have in the collection?
11. Numbers
    Write smallest three-digit number, which in division 5 and 7 gives the rest 2.
12. Divisors
    The sum of all divisors unknown odd number is 2112. Determine sum of all divisors of number which is twice of unknown numbers.
13. Bundle of candies
    In the store has 168 chocolates, caramel candies 224 and 196 hard candies. How many packages we can do and how many of candies will be in each package?
14. Combinations
    How many different combinations of two-digit number divisible by 4 arises from the digits 3, 5 and 7?
15. Unknown number
    Unknown number is divisible by exactly three different primes. When we compare these primes in ascending order, the following applies: • Difference first and second prime number is half the difference between the third and second prime numbers. • The produ
16. Theorem prove
    We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
17. Basket of fruit
    In six baskets, the seller has fruit. In individual baskets, there are only apples or just pears with the following number of fruits: 5,6,12,14,23 and 29. "If I sell this basket," the salesman thinks, "then I will have just as many apples as a pear." Which