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On the \(xy\)-plane, the origin is labeled with an \(m\). The points \((1, 0), (0, 1), (-1, 0)\) and \((0, -1)\) and  are labeled with \(m\)'s. The points\((0,2), (-1, 1), (-2, 0), (-1, -1), (0, -2),\) and \((1, -1)\) are labeled with \(t\)'s. The points \((3,0), (2,1), (1,2), (0, 3), (-1, 2), (-2, 1),\) and \((2, -1)\) are labeled with \(h\)'s. If you are only allowed to move up, down, left, and right, starting from the origin, how many distinct paths can be followed to spell the word 'math'?

 

please help :D

 

i spent a long time formatting this

 May 3, 2020
 #1
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Can you attach a diagram?

 May 3, 2020

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