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MATH / On the xy-plane, the origin is labeled with an M. The points (1,0), (−1,0), (0,1), and (0,−1) are labeled with A's. The points (2,0), (1,1), (0,2), (−1,1), (−2,0), (−1,−1), (0,−2),…

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problem

On the xyxy-plane, the origin is labeled with an MM. The points (1,0)(1,0), (−1,0)(-1,0), (0,1)(0,1), and (0,−1)(0,-1) are labeled with AA's. The points (2,0)(2,0), (1,1)(1,1), (0,2)(0,2), (−1,1)(-1, 1), (−2,0)(-2, 0), (−1,−1)(-1, -1), (0,−2)(0, -2), and (1,−1)(1, -1) are labeled with TT's. The points (3,0)(3,0), (2,1)(2,1), (1,2)(1,2), (0,3)(0, 3), (−1,2)(-1, 2), (−2,1)(-2, 1), (−3,0)(-3, 0), (−2,−1)(-2,-1), (−1,−2)(-1,-2), (0,−3)(0, -3), (1,−2)(1, -2), and (2,−1)(2, -1) are labeled with HH'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?
Plain-text mathematical notation (without MathML)
On the xy-plane, the origin is labeled with an M. The points (1,0), (−1,0), (0,1), and (0,−1) are labeled with A's. The points (2,0), (1,1), (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), (−3,0), (−2,−1), (−1,−2), (0,−3), (1,−2), 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?
Original LaTeX notation
On the $xy$-plane, the origin is labeled with an $M$. The points $(1,0)$, $(-1,0)$, $(0,1)$, and $(0,-1)$ are labeled with $A$'s. The points $(2,0)$, $(1,1)$, $(0,2)$, $(-1, 1)$, $(-2, 0)$, $(-1, -1)$, $(0, -2)$, and $(1, -1)$ are labeled with $T$'s. The points $(3,0)$, $(2,1)$, $(1,2)$, $(0, 3)$, $(-1, 2)$, $(-2, 1)$, $(-3, 0)$, $(-2,-1)$, $(-1,-2)$, $(0, -3)$, $(1, -2)$, 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?

level

Level 5

type

Counting & Probability

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Source and history

task_id
29a1f0a3-800e-5bba-9c32-084178cd1a8f
task_key
counting~5fand~5fprobability--test--29a1f0a3-800e-5bba-9c32-084178cd1a8f
task_revision_id
1
config / split
counting_and_probability / test

Official source

initial import