ParsedownCustom
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Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.
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How many such routes are there through a 20×20 grid?
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Consider the following "magic" 3-gon ring, filled with the numbers 1 to 6, and each line adding to nine.
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Working clockwise, and starting from the group of three with the numerically lowest external node (4,3,2 in this example), each solution can be described uniquely.
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For example, the above solution can be described by the set: `4,3,2; 6,2,1; 5,1,3`.
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@@ -23,4 +23,4 @@ By concatenating each group it is possible to form 9-digit strings; the maximum
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Using the numbers 1 to 10, and depending on arrangements, it is possible to form 16- and 17-digit strings.
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What is the maximum 16-digit string for a "magic" 5-gon ring?
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@@ -1,6 +1,6 @@
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By counting carefully it can be seen that a rectangular grid measuring 3 by 2 contains eighteen rectangles:
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Although there exists no rectangular grid that contains exactly two million rectangles,
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find the area of the grid with the nearest solution.
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@@ -1,7 +1,7 @@
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The points `P(x1, y1)` and `Q(x2, y2)` are plotted at integer co-ordinates and are joined to the origin,
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`O(0,0)`, to form `OPQ`.
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There are exactly fourteen triangles containing a right angle that can be formed when each co-ordinate
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lies between 0 and 2 inclusive; that is,
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@@ -10,6 +10,6 @@ lies between 0 and 2 inclusive; that is,
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0 <= x1, y1, x2, y2 <= 2.
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~~~
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Given that `0 <= x1, y1, x2, y2 <= 50`, how many right triangles can be formed?
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