The Tower of Hanoi: Difference between revisions

Latest revision as of 00:29, 27 March 2026

T_n is the minimum number of moves that will transfer n disks from one peg to another under Lucas's rules.

T₀ = 0, T₁ = 1, T₂ = 3 .....

T₀ = 0, T_n = 2T_{n - 1} + 1, for n > 0

T_n = 2ⁿ - 1, for n >= 0

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 ==== Recurrent Problems - The Tower of Hanoi ====
-T&lt;sub&gt;n&lt;/sub&gt; is the minimum number of moves that will transfer n disks from one peg to another under Lucas's rules.
+T<sub>n</sub> is the minimum number of moves that will transfer n disks from one peg to another under Lucas's rules.
 ===== small cases =====
-T&lt;sub&gt;0&lt;/sub&gt; = 0,  T&lt;sub&gt;1&lt;/sub&gt; = 1,  T&lt;sub&gt;2&lt;/sub&gt; = 3 .....
+T<sub>0</sub> = 0,  T<sub>1</sub> = 1,  T<sub>2</sub> = 3 .....
 ===== mathematical expression =====
-'''T&lt;sub&gt;0&lt;/sub&gt; = 0,   T&lt;sub&gt;n&lt;/sub&gt; = 2T&lt;sub&gt;n - 1&lt;/sub&gt; + 1, for n > 0'''
+'''T<sub>0</sub> = 0,   T<sub>n</sub> = 2T<sub>n - 1</sub> + 1, for n > 0'''
 ===== closed form =====
-'''T&lt;sub&gt;n&lt;/sub&gt; = 2&lt;sup&gt;n&lt;/sup&gt; - 1, for n >= 0'''
+'''T<sub>n</sub> = 2<sup>n</sup> - 1, for n >= 0'''