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Question Number 4105 by prakash jain last updated on 28/Dec/15

How many distinct ways are there for a knight to reach from bottom left corner of chessboard to top right corner. (knight going from square a1 to h8).

$$\mathrm{How}\:\mathrm{many}\:\mathrm{distinct}\:\mathrm{ways}\:\mathrm{are}\:\mathrm{there}\:\mathrm{for} \\ $$$$\mathrm{a}\:\mathrm{knight}\:\mathrm{to}\:\mathrm{reach}\:\mathrm{from}\:\mathrm{bottom}\:\mathrm{left}\:\mathrm{corner}\:\mathrm{of} \\ $$$$\mathrm{chessboard}\:\mathrm{to}\:\mathrm{top}\:\mathrm{right}\:\mathrm{corner}. \\ $$$$\left(\mathrm{knight}\:\mathrm{going}\:\mathrm{from}\:\mathrm{square}\:\mathrm{a1}\:\mathrm{to}\:\mathrm{h8}\right). \\ $$

Commented by Filup last updated on 29/Dec/15

Without re using the same space?

$$\mathrm{Without}\:\mathrm{re}\:\mathrm{using}\:\mathrm{the}\:\mathrm{same}\:\mathrm{space}? \\ $$

Commented by Filup last updated on 29/Dec/15

Chess board B is 8x8. B therefore has 64 squares. The knight/horse K can move 2×1 or 1×2 spaces a time. Moving down 2 each step is 4 moves Moving horizontal 2 each step is 4 moves ∴You can reach the further most row/column in ≥4 moves Alternating gives you: −???− −continue− i shall continue to think

$$\mathrm{Chess}\:\mathrm{board}\:{B}\:\mathrm{is}\:\mathrm{8x8}. \\ $$$${B}\:\mathrm{therefore}\:\mathrm{has}\:\mathrm{64}\:\mathrm{squares}. \\ $$$$ \\ $$$$\mathrm{The}\:\mathrm{knight}/\mathrm{horse}\:{K}\:\mathrm{can}\:\mathrm{move} \\ $$$$\mathrm{2}×\mathrm{1}\:\mathrm{or}\:\mathrm{1}×\mathrm{2}\:\mathrm{spaces}\:\mathrm{a}\:\mathrm{time}. \\ $$$$ \\ $$$$\mathrm{Moving}\:\mathrm{down}\:\mathrm{2}\:\mathrm{each}\:\mathrm{step}\:\mathrm{is}\:\mathrm{4}\:\mathrm{moves} \\ $$$$\mathrm{Moving}\:\mathrm{horizontal}\:\mathrm{2}\:\mathrm{each}\:\mathrm{step}\:\mathrm{is}\:\mathrm{4}\:\mathrm{moves} \\ $$$$\therefore\mathrm{You}\:\mathrm{can}\:\mathrm{reach}\:\mathrm{the}\:\mathrm{further}\:\mathrm{most}\: \\ $$$$\mathrm{row}/\mathrm{column}\:\mathrm{in}\:\geqslant\mathrm{4}\:\mathrm{moves} \\ $$$$ \\ $$$$\mathrm{Alternating}\:\mathrm{gives}\:\mathrm{you}: \\ $$$$−???− \\ $$$$ \\ $$$$−\mathrm{continue}− \\ $$$$\mathrm{i}\:\mathrm{shall}\:\mathrm{continue}\:\mathrm{to}\:\mathrm{think} \\ $$

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