Let f（n） is number of ways by which we place the numbers from 1 to 2n in a 2×n rectangle and place 1 on top-left cell.We can easily get the recursion f（n＋1）=f（n）＋1.Since f（1）=1, We can get f（n）=n.On the other hand, if we place 1 on the cell whose column is k（1＜k＜n）, the number of ways is f（k－1）＋f（n－k）=n－1.Therefore, whole number of ways is 4n＋(n－1)・(2n－4)=2n^2－2n＋4.This problem case is n=50, so 2・50^2－2・50＋4=4904.

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question : (a) What does recursion mean ? (b) What's a recursion relation ?

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. Thanks , kk108 .

Hello, kk108! I am not good at english.So, I cannot understand your questions. What's the 'trivial' mean? You said that this problem is trivial?

@above , trivial means easy . What I meant was that , you were saying that you used something called recursion, to solve that problem; so my question was , what does recursion mean ?This word was used in my math book as 'recurrence relation '; that's why I am asking . Thanks , kk108.

I used the word 'recursion' as recurrence relation. By the way, how about your solution for this problem?