MathDB

Problem 1

Part of 2023 Kyiv City MO Round 1

Problems(5)

Rectangle cut into 6 squares

Source: Kyiv City MO 2023 Round 1, Problem 7.1

12/16/2023
The rectangle is cut into 6 squares, as shown on the figure below. The gray square in the middle has a side equal to 1. What is the area of the rectangle?
https://i.ibb.co/gg1tBTN/Kyiv-MO-2023-7-1.png
geometryrectangle
Best algebra in the history of MO

Source: Kyiv City MO 2023 Round 1, Problem 9.1

12/16/2023
Find the integer which is closest to the value of the following expression:
((3+1)2023−(13−1)2023)⋅((3+2)2023−(13−2)2023)⋅…⋅((3+8)2023−(13−8)2023)\left((3 + \sqrt{1})^{2023} - \left(\frac{1}{3 - \sqrt{1}}\right)^{2023} \right) \cdot \left((3 + \sqrt{2})^{2023} - \left(\frac{1}{3 - \sqrt{2}}\right)^{2023} \right) \cdot \ldots \cdot \left((3 + \sqrt{8})^{2023} - \left(\frac{1}{3 - \sqrt{8}}\right)^{2023} \right)
algebra
Close integer

Source: Kyiv City MO 2023 Round 1, Problem 8.1

12/16/2023
Find the integer which is closest to the value of the following expression:
((7+48)2023+(7−48)2023)2−((7+48)2023−(7−48)2023)2((7 + \sqrt{48})^{2023} + (7 - \sqrt{48})^{2023})^2 - ((7 + \sqrt{48})^{2023} - (7 - \sqrt{48})^{2023})^2
algebraexpression
Inequality with number $2023$

Source: Kyiv City MO 2023 Round 1, Problem 10.1

12/16/2023
Find all positive integers nn that satisfy the following inequalities:
−46≤202346−n≤46−n-46 \leq \frac{2023}{46-n} \leq 46-n
inequalities
Compare A and B

Source: Kyiv City MO 2023 Round 1, Problem 11.1

12/16/2023
Which number is larger: A=19:120233A = \frac{1}{9} : \sqrt[3]{\frac{1}{2023}}, or B=log⁡202391125B = \log_{2023} 91125?
algebraCompare