The "New" Knight

Logic Level 1

A new piece in chess has been introduced. Instead of being like the knight, which moves two spaces horizontally and one space vertically or two spaces vertically and one space horizontally, the new piece moves three spaces horizontally and one space vertically or three spaces vertically and one space horizontally.

The piece is now on the square labelled "A". What is the least number of moves it needs to have to get to the square labelled "B"?

2 3 4 5

3 solutions

Arul Kolla
May 30, 2016

Relevant wiki: Chess Puzzles

The solution is shown below. There is no way to do it with less than 3 moves.

Cute problem. Can you also explain why there is no solution in less moves and how many solutions for the number of 3 moves are for your problem anyways ?

A A - 5 years ago

@Arul Kolla , A A posed a valid question, can you show that "2" is not possible?

Pi Han Goh - 5 years ago

as this knight can only move either I or 3 we can see the movements are pretty much similar to position vectors now taking x and y axis , and origin as point A it has to reach B which is point 1,-1 separating the x and y vector components of its path they must add up to 1 and -1 respectively the vectors can have the magnitude +3,+1,-3,-1, now clearly any 2 of these cannot be added to give 1 or -1 so we will need atleast 3 moves nevertheless some hit and trial approach will be required later in the solution but 2 moves are clearly not sufficient

Shaurrya Lakhanpal - 5 years ago

@Shaurrya Lakhanpal – Yes , that's a way of thinking technically at it. You can still show it without any elaborated concepts and just by thinking in the terms of the problem anyway.

A A - 5 years ago

There are 4 possible moves in first turn. Then you whatever position you pick, you need a move that it can move it to either 4 or 2 vertically blocks + 0 or 2 horizontally. Since the camel cannot establish such a move for this turn to go to B, hence 2 turns are impossible. Note: When I said " either 4 or 2 vertically etc... , I was referring to the roadpath of the camel to B".

Nikolas Кraj - 1 year, 9 months ago

By showing that it is impossible you will point precisely to what makes it impossible anyway. Considering this , the reason for which it is impossible will be distinguished clearly I mean anyway.

A A - 5 years ago

Alex Li
Jun 3, 2016

It can be done in 3 moves with something such as c2,b5,e4

To prove it can't be done in less moves:

Trial and Error shows it can't be done in 1

Considering only vertical movement, the piece either moves up 3, 1, -1, or -3.

It needs to be moved -1.

No combination of any 2 of these odd numbers will create another odd. (By this argument, it also can't be done in 4, 6, 8, etc. moves)

Your argument is cute but it doesn't also explain why it can't be done in 1 move without trial and error anyway , just be a little subtle in thinking.

In order to cover both , the possibilities of moves in 1 and 2 , consider the possible places on which you can arrive at both squares A and B and yo will deal with all of them anyway.

Edit : sorry , I wasn't attentive.

It's indeed trial and error but you can put it even clearer.

A A - 5 years ago

Shaurrya Lakhanpal - 5 years ago

Vishal Mittal
Jul 16, 2018

Application of BFS algorithm to find shortest path. (similar to code posted by João Areias , 22, Brazil in level 2 tactical).

Here is C++ implementation : https://ide.geeksforgeeks.org/5HizN5pHax

The "New" Knight

3 solutions

0 pending reports