Crocodile chooses $1$ x $4$ tile from $2018$ x $2018$ square.The bear has tilometer that checks $3$x$3$ square of $2018$ x $2018$ is there any of choosen cells by crocodile.Tilometer says "YES" if there is at least one choosen cell among checked $3$ x $3$ square.For what is the smallest number of such questions the Bear can certainly get an affirmative answer?
Problem
Source: izho2018
Tags: combinatorics, combinatorics unsolved, Tiling
qweDota
14.02.2018 08:51
$\frac{673^2 -1}{2}$
CROWmatician
08.01.2022 03:28
bump, any solution?
FaThEr-SqUiRrEl
08.01.2022 03:29
CROWmatician wrote: bump, any solution? do you?
MerlinLegion07
09.02.2022 13:14
have you any solution?
MerlinLegion07
09.02.2022 14:35
I have a solution,but I don't know:this solution is true or false if we place 3X3 square in this case: we let 3X3 black and notplaced is white we place this square as chessboard (we have 2018=673x3 -1 that's why we let 2019x2019 not changed at least question) from this 2019/3=673 we have 673x673 chess board we determine black cage:337 x337 +336x336=226 465
douglasmorales
01.04.2022 16:21
6.732 – 2/2 Converting the decimal into fraction (673/100)2-1/2 For raising a fraction to a power we have to rise the numerator and denominator to that power 6732/1002 -1 /2 By writing numerator above common denominator 6732 – 1002 / 1002 / 2 To factor the expression we use a2 – b2 = (a - b) (a + b) (673 - 100) × (673 + 100) / 1002 / 2 By subtracting the numbers 573 (673 + 100) / 1002 / 2 On the other hand we will add the numbers 573 × 773 / 1002 / 2 Now we will multiply the number 573 × 773 / 1002 / 2 442929 / 1002 / 2 Simplifying the complex fraction: 442929 / 2 × 1002 By evaluating the powers 442929 / 2 × 10000 By multiplying the numbers 442929 / 20000 Solution: 2214645