We solve problems

Problems Discrete Mathematics Set theory and logic Mathematical logic Puzzles

Solve the rebus \(AC \times CC \times K = 2002\) (different letters correspond to different integers and vice versa).

Problems Discrete Mathematics Set theory and logic Mathematical logic Puzzles

Rebus. Solve the numerical rebus \(AAAA-BBB + SS-K = 1234\) (different letters correspond to different numbers, but the same letters each time correspond to the same numbers)

Problem #PRU-103784

Problems Discrete Mathematics Set theory and logic Mathematical logic Puzzles

11–11 2.0

When Harvey was asked to come up with a problem for the mathematical Olympiad in Sunny City, he wrote a rebus (see the drawing). Can it be solved? (Different letters must match different numbers).

Problem #PRU-103812

Problems Number Theory Arithmetic operations. Number identities Discrete Mathematics Set theory and logic Mathematical logic Puzzles

11–11 2.0

Alex laid out an example of an addition of numbers from cards with numbers on them and then swapped two cards. As you can see, the equality has been violated. Which cards did Alex rearrange?

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-109423

Problems Discrete Mathematics Set theory and logic Mathematical logic Puzzles Number Theory Divisibility The fundamental theorm of arithmetic. Prime factorisation.

11–12 2.0

At the end of the term, Billy wrote out his current singing marks in a row and put a multiplication sign between some of them. The product of the resulting numbers turned out to be equal to 2007. What is Billy’s term mark for singing? (The marks that he can get are between 2 and 5, where 5 is the highest mark).

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).

Problem #PRU-115707

Problems Discrete Mathematics Set theory and logic Mathematical logic Puzzles

11–13 2.0

Can I replace the letters with numbers in the puzzle \(RE \times CTS + 1 = CE \times MS\) so that the correct equality is obtained (different letters need to be replaced by different numbers, and the same letters must correspond to the same digits)?

Problem #PRU-116460

Problems Number Theory Arithmetic operations. Number identities Discrete Mathematics Set theory and logic Mathematical logic Puzzles

10–11 2.0

Pinocchio correctly solved a problem, but stained his notebook. \[(\bullet \bullet + \bullet \bullet+1)\times \bullet= \bullet \bullet \bullet\]

Under each blot lies the same number, which is not equal to zero. Find this number.

Problem #PRU-116468

Problems Number Theory Numeral systems Decimal number system Discrete Mathematics Set theory and logic Mathematical logic Puzzles

10–11 2.0

Peter recorded an example of an addition on a board, after which he replaced some digits with letters, with the same figures being replaced with the same letters, and different figures with different letters. He did it such that he was left with the sum: \(CROSS + 2011 = START\). Prove that Peter made a mistake.