Below is given a figure, in which a horse is placed on one of the boxes in a square grid of size $5 \times 5$. The horse can move in either of the following ways in a single move: (i) two boxes to either left or right side and one box to either up or down side (ii) two boxes to either up or down side and one box to either left or right side (iii) the horse cannot step on a grey box. The horse has to stay within the grid and any move to out of the grid is NOT legal. How many white boxes are there which cannot be covered by horse within 3 moves?
To solve this problem, we need to determine the number of white boxes that cannot be covered by the horse within 3 moves on the given grid. The horse moves like a knight in chess, and certain squares are greyed-out and cannot be stepped on.
Movement Rules:
- The horse can move two boxes in one direction and one box in a perpendicular direction.
- The horse cannot step on grey boxes and must stay within the grid.
Steps to Solve:
- Identify possible starting positions and moves from the horse's initial starting point.
- Move the horse to each new position and record which white boxes are covered after each move (up to 3 moves).
- Repeat the process, ensuring that no grey boxes are counted and all moves remain within bounds.
- Count all white boxes that cannot be reached within 3 moves.
After analyzing the movements:
- First move: Cover specific positions. Possible squares in contact are computed considering avoided grey cells.
- Subsequent moves expand the covered positions further considering the knight moves and grid boundaries.
Following this approach through all legal moves and combinations, we determine that there are 3 white boxes that remain uncovered after 3 moves.
Hence, the correct answer is the number of white boxes that cannot be covered by the horse within 3 moves is 3.
Important Questions from Logical Puzzle
- Six persons Raj, Rohit, Rachit, Rajat, Rishu, and Rinku are working in an office. Each of them has a favorite car viz. P, Q, R, S, T, and U, but not necessarily in the same order. Each of them got a different salary - 1000, 2000, 2500, 3000, 3500, and 4000, but not necessarily in the same order. Rajat gets a salary of 2500 and his favorite car is U. The one who likes car Q gets a salary of 3000. Rachit likes car P and gets a salary of 3500. The one who gets a salary of 1000 does not like car R or S. Rinku does not like car Q or S but gets a salary of 2000. Rishu gets a salary of 4000 and does not like a car R. Rohit does not get a salary of 1000. Who gets a salary of 3000?
- Six friends P, Q, R, S, T, and U are sitting at different positions in a row of the company, and each of them get a different salary viz – 500, 800, 1000, 1500, 1800 & 2000, but not necessary in the same order. The friend who gets a salary of 2000 does not sit at the extreme end of the row. Q sits immediately before R and gets a salary of 800. T sits between U and S. Q is second to the left of S. P sits at the left end of the row and gets a salary of 1000. T gets a salary of 1500. R gets a salary neither of 2000 nor of 1800. How much salary does U get?
- Seven men A, B, C, D, E, F and G are standing in a queue, one behind the other in that order. That is, A is first in queue while G brings up the rear. Each of them is wearing a hat of a different colour of the rainbow - Violet, Indigo, Blue, Green, Yellow, Orange, and Red, but not necessarily in that order. It is also known that:
• D can see in front of him green and blue hats, but not the violet hat.
• E can see violet and yellow hats, but not the red hat.
• G can see hats of all the colours except Orange.
• E is wearing the Indigo coloured hat.
What colour hat is worn by F? - Who amongst the females arrived third?
- Which is the correct pair of husband and wife?
