C. Two answers

1. If p is the perimeter of a right angle triangle with integral length sides, {a, B, c}, there are exactly three solutions for p = 120. click

{, 52}, {, 51}, {, 50}

For which value of p <= 1000, is the number of solutions maximized?

The translation is:

If p is such a number, the sum of the three tuples {a, B, c} is p, and a, B, and c can form three edges of a right triangle. When p = 120, there are three solutions:

{, 52}, {, 51}, {, 50}

What is the maximum number of p solutions that meet the preceding conditions within p <= 1000?

Answer: 840.

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2. A permutation is an ordered arrangement of objects. for example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. if all of the permutations are listed numerically or alphabetically, we call it lexicographic order. the lexicographic permutations of 0, 1 and 2 are:

012 021 102 120 201 210

What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9? Click

A permutation is an ordered arrangement of objects. For example, 3124 is a possible arrangement of numbers 1, 2, 3, and 4. It is called a dictionary order to list all numbers or letters. The dictionary sorting of numbers 0, 1, and 2 is:

012 021 102 120 201 210

What are the 1,000,000th (1 million) lexicographic sorting numbers of numbers?

Answer: 2783915460 {code placeholder}