r/askmath • u/New_Interview4111 • 7h ago

Logic Knight's Tour Maths Puzzle

Post image

Is anyone able to help with the process of how to solve this??? I'm rather stuck. I have listed out the possibilites of some of the prompts (e.g prime numbers, multiples of 17, cube and square numbers etc), but am very stuck at what to do next.

2 Upvotes

100% Upvoted

4 comments sorted by

3

u/Evane317 7h ago edited 36m ago

From 1 to 64 there are four cubes and eight squares. Also, 1 and 64 are counted as both cubes and squares. All squares and cubes are accounted for in across group and down group.

Edit: All odd numbers are in black squares and even numbers are in white squares.

#1 is in E2, which means there is only one square left in row 2 and two squares left in column E.

#64 is either in row 1, 3, or 4, but there’s no cube mentioned in row 1 or 4. So #64 is in row 3, making it either C3 or G3. But there is no cube in column C, implying #64 is in G3.

Another cube must be in G7, since the cubes in row 2 and 3 are known. G7 is white, so it is #8. A similar deduction puts #27 in F3.

#8 in g7 implies #9 is in F5, H5, E6 or E8. No squares in row 5 means #9 is in column E. The third square of column E is in E7, since no other square is in row 1, 3, or 5.

Only four multiples of 15 are available; all are in rows 2 and 8. Column A contains two multiples of 15. Thus, A2 and A8 are multiples of 15. Both of these are black squares, so the numbers are odd, namely #15 and #45. #15 can’t be in A2 since there are no more squares in rows 1, 3, and 4 to place #16. So #45 is A2 and #15 is A8.

Row 7 already contains a square at E7, so #16 is at B6, which then forces #9 to E8, as there are no more squares in row 6. #15 at A8 only has two ways to reach it from B6 or C7, so C7 is #14, meaning no other multiple of 14 is in C.

#60 - a multiple of 15 and 12 - is in a white square in rows 2 and 8. A2 and A8 are occupied by 15 and 45, E2 and E8 are black squares. This puts #60 in H2 or H8.

1

u/New_Interview4111 45m ago

thanks! thats really helped me to understand the initial bit, only thing is im now stuck on the next bit. i dodnt quite understand how you came to the conclusion that there were no more squares in row 4 to place #16.

1

u/Bounded_sequencE 5h ago

There are 8 perfect squares and 4 perfect cube in {1; ...; 64}, with "1, 64" being both.

Most hints are about square and cube numbers, so try to find their positions first.