Logic Riddles for Chess Players (3)

by Arne Kaehler
5/9/2020 – This is the third entry of logic riddles for chess players. In this case the riddle is a bit different compared to the previous logic riddles. It doesn't require too much mathematical skill and some people have a very hard time solving it. Others can find the answer in a finger snip. Keep in mind, you don't need a chess board for the solution, just your imagination and cleverness.

The modern Two Knights The modern Two Knights

The Two Knights Defence is one of the oldest opening lines in chess history. This DVD is aimed at players of both sides, giving an objective overview of all relevant theoretical lines.

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The slowest knight wins!

 

Once upon a time, there were two brothers (the black and the white pawn) who were spending their life in the kingdom (the chessboard) of their father (the ♔). One of their favourite activities was racing to the eighth row with their fast horses (the ♘ and the ♞). Sometimes the white pawn won with his ♘, on other days the black pawn won with his ♞.

The ♔ approached both of them one day, telling them:

"My dearest sons. I can sense the breath of death coming closer to get me. My life will soon be no more. Only one of you shall inherit my wonderful kingdom with all the beautiful black and white squares. Listen to me carefully:

You shall have a race from the first to the eighth row. The one whose knight reaches the eighth row as the second one, will own the kingdom.

Now, on your horses and off you go!"

With that, the king sat next to them to watch them jump on their horses and not move a single bit, looking at each other anxiously and baffled.

Can you come up with a solution to get them out of their miserable situation?

To get things clear. Although this is a chess game metaphor, there is no capturing or other chess like things, like a "knight's move" or checking the king. It is just the analogy to carry out the riddle.

So it is best to not attempt anything "chess" related for solving.

The black or white solution

Thank you again for the strong participation in the last logic riddle for chess players!

The solution has left some space to be debated, but I personally think it is very logical after all. The original question of "When will the white rooks capture a black rook?" is a bit thin, I agree. Nonetheless, some people could find the solution anyway.

Dumbing the question down to find the answer is key. Instead of thinking about sixteen rooks in total, try to make it the least possible amount, which would be two. If there had been only two rooks, one black and one white, the solution would be pretty straightforward with the white rook knowing, that there can be only one white rook for sure, so he would capture the black rook in the first evening.

There can neither be two black rooks, because the chess player sees a white rook, or two white rooks, because they wouldn't be able to fulfil the task, capturing a black rook. 

We can have the same logic working for four rooks and carry on with the same pattern.

If two of the four rooks were white, they would wait two days.

Spinning this up to sixteen rooks on the chess board gives the solution which one of our readers found:

varunkulkarni 4/30/2020 06:25
On the 7th day post 7 pm, every white rook would know that they are a white rook as no one else has spoken on the 7th day at 7pm. So on the 8th day at 7 pm, any white rook can make a move and capture a black rook ?

Correct! After eight days, all of them are absolutely sure and can capture a black rook.

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Arne Kaehler, a creative thinker who is passionate about board games in general was born in Hamburg and learned how to play chess at a very young age. Through teaching chess to youth teams and creating chess content on YouTube, Arne was able to extend this passion onto others and has even made an online chess course for anyone who wants to learn how to play this game. Currently, Arne blogs for the English news page of ChessBase and focuses on creating promotional and entertaining articles.
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JoshuaVGreen JoshuaVGreen 5/11/2020 05:18
The wP races with his Knight to the eighth row. Upon arriving there first, he promotes himself to a Knight, thereby becoming the second horse there. :P
varunkulkarni varunkulkarni 5/10/2020 04:10
Exchange horses!
timagw timagw 5/10/2020 02:37
The last (second) knight/horse wins. They have to interchange the horses. Black pawn will ride white horse and white pawn to ride black horse. The race will be over in normal time as they will try to keep their own horse behind. And if white horse is first, black pawn will inherit and vice versa.
JoshuaVGreen JoshuaVGreen 5/9/2020 11:51
@Justjeff, the Rook puzzle was excessively complicated by the addition of the chess elements. Let me try to simplify it:

There are eight Rooks on the board. Each is White, but no Rook knows its own color. However, every Rook can see every other Rook and knows its color as well as what actions -- if any -- it takes. A player comes up one morning and orders that, at 7:00PM each day, any Rook that (then) KNOWS it's White must leave the board immediately. He then adds that he sees at least one White Rook. What will happen?

It's easy to think "nothing" since the player (apparently) hasn't told the Rooks anything they don't already know, but in fact they now know that every other Rook knows there's a White Rook, that every other Rook knows that every other Rook knows that there's a White Rook, that every other Rook knows that every other Rook knows that every other Rook knows that there's a White Rook, etc.. To see why this helps, think about smaller cases:

- If there were only one White Rook, that Rook would immediately know its color and would leave at 7:00PM.
- If there were two White Rooks, say A and B, neither would do anything the first night. However, upon seeing that B doesn't leave at 7:00PM, A would realize that B must have seen some other White Rook, hence A would have to be White. B would follow the same logic, and both would leave at 7:00PM on the second night.
- If there were three White Rooks, say A, B, and C, then each can reduce to the previous case. That is, A reasons that if he's Black then B and C will both leave on the second night. Since neither does, A then realizes that he must be White, and all the Rooks will leave on the third night.

The above logic continues through to eight White Rooks; they'll all leave the board on the eighth night.
Justjeff Justjeff 5/9/2020 06:23
I also thought of the solution presented to the white/black rook problem but believe it is not correct.

It would be correct if the human sees a *different* white rook each night, but all he says is that he sees a white rook. It could be the same rook each evening, so starting on Day 2 the statement provides no new information.
JoshuaVGreen JoshuaVGreen 5/9/2020 04:03
(Also, language ambiguity leaves it unclear if the standard solution satisfies the instruction given by the King right before he sat down to watch.)
JoshuaVGreen JoshuaVGreen 5/9/2020 03:41
This is another one that I've seen before. I know the intended answer, but can we be sure that the Knights will behave?
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