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

$$\mathrm{How}\mathrm{many}\mathrm{distinct}\mathrm{ways}\mathrm{are}\mathrm{there}\mathrm{for}$$$$\mathrm{a}\mathrm{knight}\mathrm{to}\mathrm{reach}\mathrm{from}\mathrm{bottom}\mathrm{left}\mathrm{corner}\mathrm{of}$$$$\mathrm{chessboard}\mathrm{to}\mathrm{top}\mathrm{right}\mathrm{corner}.$$$$\left(\mathrm{knight}\mathrm{going}\mathrm{from}\mathrm{square}\mathrm{a}1\mathrm{to}\mathrm{h}8\right).$$

Commented by Filup last updated on 29/Dec/15

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

Commented by Filup last updated on 29/Dec/15

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

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