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As a start (and possibly as an equivalent proof?) you can mentally brute force it by cutting the board down to 4x4 and just visualising how the blocks might fit. It quickly becomes obvious that it's not possible.
This problem reminds me of another problem. There is a round table and two players, A and B. The players take turns placing a coin on the table in any location they desire, but coins may not overlap. The first person who is unable to place a coin loses. What is the winning first move? Answer: the winning move is for player A to place the first coin in the center of the table. After that, no matter which location play…
If you place a coin in the center, then due to symmetry there must be an even number of remaining places for a coin (or you didn't put it in the center).
You can work up from remaining=2 to see that player A always wins with an even remainder.
I like the infamous Von Neumann "Fly and the trains" math/physics problem - mainly because it's very easy to solve the easy way, or you can go about it the harder way. And apparently Von Neumann did it on the spot, the harder way, almost instantaneous. It goes like this (stolen from a website - there are many variations on this): Problem: Two trains are on the same line, 60 miles apart, heading towards each other, ea…
100 ants are spaced evenly on a 1m stick. They travel at 1m/minute. When an ant bumps into another ant, they both turn around and go the other way. When an ant reaches the end of the stick it falls off.
How long before all the ants fall off?
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A nuance here is that you are assuming the existence of a solution. It may be the case there are no values for A to J that can result in that equation. Iterating through all possibilities shows that the solution exists, the proof in the tweet doesn't.
The proof in the tweet gives steps to getting a solution, and the solution works. In what way is that not showing that the solution exists?
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The proof in the tweet gives steps to getting a solution, and the solution works. In what way is that not showing that the solution exists?
The tweet only shows what J is, conditional on that there is a solution.
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The tweet only shows what J is, conditional on that there is a solution.
Isn't that exactly how any constructive proof works?
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The tweet only shows what J is, conditional on that there is a solution.
Isn't that exactly how any constructive proof works?
In that case, it has been shown that if a solution exists, it must be that J=6. With this additional information, you can try and find the other digit and conclude the proof (or in the case there's no solution, reach a contradiction).
I don't know how this type of proof is called in English but it's quite common. First come up with necessary conditions on your potential solution, and then you use these conditions to build an actual solution.
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The tweet only shows what J is, conditional on that there is a solution.
Isn't that exactly how any constructive proof works?
ABC
DEF
+ GHI
----------
12300000J
It's an interesting probability question in its own right, as it has a hugely counter-intuitive correct answer in my opinion. But the sh*storm it caused is equally interesting. Hence I will share this article which covers both aspects:
https://priceonomics.com/the-time-everyone-corrected-the-wor...
A major takeaway - statistics and probability can be really tough sometimes and even world class practitioners can be caught out when intuition and mathematics clash. And a little humility is perhaps wise when trying to "correct" people, just in case...
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What? The mathematics shows correctly on the page for me, and that PDF is missing some chessboard images...
presumably they are running a script blocker that took out the JS that renders the maths.