We solve problems

Problem #PRU-88001

Problems Methods Algebraic methods Processes and operations Discrete Mathematics Algorithm Theory Theory of algorithms (other)

11–13 3.0

A traveller rents a room in an inn for a week and offers the innkeeper a chain of seven silver links as payment – one link per day, with the condition that they will be payed everyday. The innkeeper agrees, with the condition that the traveller can only cut one of the links. How did the traveller manage to pay the innkeeper?

Problem #PRU-88031

Problems Methods Algebraic methods Processes and operations Discrete Mathematics Algorithm Theory Theory of algorithms (other)

10–13 3.0

There are 6 locked suitcases and 6 keys for them. It is not known which keys are for which suitcase. What is the smallest number of attempts do you need in order to open all the suitcases? How many attempts would you need if there are 10 suitcases and keys instead of 6?

Problem #PRU-64494

Problems Methods Algebraic methods Proof by exhaustion Discrete Mathematics Set theory and logic Mathematical logic Puzzles

10–11 2.0

Specify any solution of the puzzle: \(2014 + YES =BEAR\).

Problem #PRU-87992

Problems Number Theory Numeral systems Decimal number system Methods Algebraic methods Proof by exhaustion

10–12 2.0

One three-digit number consists of different digits that are in ascending order, and in its name all words begin with the same letter. The other three-digit number, on the contrary, consists of identical digits, but in its name all words begin with different letters. What are these numbers?

Problem #PRU-88071

Problems Number Theory Divisibility Division with remainders. Arithmetic of remainders Division with remainder Methods Algebraic methods Proof by exhaustion

10–12 2.0

Find all of the natural numbers that, when divided by 7, have the same remainder and quotient.

Problem #PRU-88081

Problems Number Theory Numeral systems Decimal number system Methods Algebraic methods Proof by exhaustion

10–12 2.0

Write the first 10 prime numbers in a line. How can you remove 6 digits to get the largest possible number?

Problem #PRU-88120

Problems Methods Algebraic methods Counting in two ways Fun Problems Word Problems Tables and tournaments Number tables and its properties

10–12 2.0

Is it possible to fill a \(5 \times 5\) table with numbers so that the sum of the numbers in each row is positive and the sum of the numbers in each column is negative?

Problem #PRU-103882

Problems Methods Algebraic methods Proof by exhaustion Discrete Mathematics Set theory and logic Mathematical logic Puzzles

11–12 2.0

Find the smallest four-digit number \(CEEM\) for which there exists a solution to the rebus \(MN + PORG = CEEM\). (The same letters correspond to the same numbers, different – different.)

Problem #PRU-115489

Problems Discrete Mathematics Set theory and logic Mathematical logic Mathematical logic (other) Methods Algebraic methods Proof by exhaustion

10–12 2.0

One day, Claudia, Sofia and Freia noticed that they brought the same toy cars to kindergarten. Claudia has a car with a trailer, a small car and a green car without a trailer. Sofia has a car without a trailer and a small green one with a trailer, and Freia has a big car and a small blue car with a trailer. What kind of car (in terms of colour, size and availability of a trailer) did all of the girls bring to the kindergarten? Explain the answer.

Problem #PRU-115492

Problems Methods Algebraic methods Proof by exhaustion Discrete Mathematics Set theory and logic Mathematical logic Puzzles

11–13 2.0

The \(KUB\) is a cube. Prove that the ball, \(CIR\), is not a cube. (\(KUB\) and \(CIR\) are three-digit numbers, where different letters denote different numbers).