?? Q?/

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There is a rectangle with m vertical lines and n horizontal lines (taking the edges too).

Find the no.of ways in which a pencil can travel from the North-West to the South-East corner going through the shortest possible distance.
Note: The pencil can only travel on the lines..

#Mathematics #Algebra

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Aditya Bhutra ·2012-02-22 08:23:24

it is a known result - (m+n)!m!n!

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Sigma ·2012-02-22 09:12:46

I could not understand the explanation given in the book. can u give some more hints to this..?

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Swaraj Dalmia ·2012-02-22 09:53:23

It is explained here: http://joaoff.com/2008/01/20/a-square-grid-path-problem/

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samagr@ ·2012-02-24 09:09:00

just consider the no of arrangements the word (UUUUUU... m times)(RRRRRRRR... n times)
U being UP direction , R being RIGHT direction

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Sigma ·2012-02-26 08:50:21

thanks

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Basic Integral Calculus Operators Symbols Matrix Cases

√ √ || {} [] () → ~ ^ x x x → → ln log lg lim lim cos sin tan cot arcsin arccos arctan

∫ ∫ ∫ ∫ ∫ ∬ ∬ ∬ ∬ ∬ ∭ ∭ ∭ ∭ ∭ ⨌ ⨌ ⨌ ⨌ ⨌

∑ ∑ ∑ ∑ ∑ ∮ ∮ ∮ ∮ ∮ ∏ ∏ ∏ ∏ ∏ ∐ ∐ ∐ ∐ ∐

+ - × ÷ ± ∓ = ∪ ∩ ≠ ∼ ≈ ∅ ∀ ∃ ∈ ∋ ∝ ≤ ≥ ≃ ≅ ≡ < > ≪ ≫ ⊂ ∉ ⊃ ⊆ ⊇ ⇒ ⇐ ⇔ ⇒ ⇐ ⇔ ⇑ ⇓ ⇕ → ← ↔ → ← ↔ ↑ ↓ ↕ ↖ ↗ ↘ ↙ ↪ ↩ ⇀ ↼ ⇁ ↽

° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω

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