Pure maths, physics, chemistry, etc.: brain-training tasks that have nothing to do with trade [Part 2] - page 13
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Strong... Another one, then:
A corner square has been cut out of a chessboard. Is it possible to cover the rest of the board completely with 1x3 squares of cardboard?
Strong... Another one, then:
A corner square has been cut out of a chessboard. Is it possible to cover the rest of the board completely with 1x3 squares of cardboard?
That one is undecided and this one went straight away
It's a cool task. It's not very difficult, I solved it quickly. But the wording is beautiful.
Megamind came up with a ten-digit natural number. The first (left) digit of that number equals the number of zeros in its entry, the second digit equals the number of ones, the third equals the number of twos, etc., the last digit equals the number of nines in the entry of that number. Can you repeat Megamind's achievement and find this number?
Let me also post a problem from a famous forum.
The weight of the problem is 4.
The invaders, in a way known only to them, choose two different real numbers and write them on two pieces of paper. Then they invite Megamind to choose any piece of paper, look at the number written there and guess whether the number on the other piece of paper is higher or lower. Prove that Megamind has a strategy that will allow him to guess with a probability greater than 50%.
A guessing strategy with a probability of an exact answer greater than 50% exists (according to the moderators). I can't decide it myself.
Strong... Another one, then:
A corner square has been cut out of a chessboard. Is it possible to cover the rest of the board completely with 1x3 squares of cardboard?
Not an interesting problem, you can code a solution, but code something useful, which is what I'm doing now.
Where can I see the sequel?
I looked and couldn't find it. Anyway, in the second picture, the cat misses and flies into the wall, saying, "There's been another miscalculation".
It's not an interesting problem, you could code a solution, but it's better to code something useful, which is what I'm doing now.
There is no solution...Number the fields of the chessboard with numbers from 1 to 8 from left to right, in each row. After cutting out a corner square, the sum of all the numbers on the board is not divisible by 3. Whereas, the sum of the numbers covered by the 1x3 cardboard is divisible by 3.
No solution...Number the fields of the chessboard with numbers from 1 to 8 from left to right, in each row. After cutting out the corner square, the sum of all the numbers on the board is not divisible by 3. Whereas, the sum of the numbers covered by the 1x3 cardboard is divisible by 3 .
Wow! Is this some kind of trademark trick of professional parquet planners?
No solution...Number the fields of the chessboard with numbers from 1 to 8 from left to right, in each row. After cutting out the corner square, the sum of all the numbers on the board is not divisible by 3. Whereas, the sum of the numbers covered by the 1x3 cardboard is divisible by 3 .
Vi is beautiful... Did you make that up?
Probably came up from a long time ago in mat school. They taught us tricks like that.