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Q&A #1592

Teachers' Lounge Discussion: Lego blocks as problem solving tool

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From: jack <jackfeb2012@gmail.com>
To: Teacher2Teacher Public Discussion
Date: 2013021120:43:22
Subject: Please explain me how to solve and what approach i should use to solve these problems

	
You have 4 types of lego blocks, of sizes 1 * 1 * 1, 1 * 1 * 2, 1 * 1
* 3 and 1 * 1 * 4. Assume you have infinite number of blocks of each
type.

You want to make a wall of height N and width M out of these blocks.
The wall should not have any holes in it. The wall you build should be
one solid structure. A solid structure means that it should not be
possible to separate the wall along any vertical line without cutting
any lego block used to build the wall. The blocks can only be placed
horizontally. In how many ways can the wall be built?

Input:
The first line contains the number of test cases T. T test cases
follow. Each case contains two integers N and M.

Output:
Output T lines, one for each test case containing the number of ways
to build the wall. 
Sample Input:
4
2 2
3 2
2 3
4 4

Sample Output:
3
7
9
3375

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