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코딩 연습
Three distinct points are plotted at random on a Cartesian plane, for which \(-1000 \le x, \; y \le 1000\), such that a triangle is formed. Consider the following two triangles: \[ {\rm A}(-340,\; 495), \; {\rm B}(-153, \;-910), \; {\rm C}(835, \; -947)\] \[ {\rm X} (-175, \; 41),\; {\rm Y}(-421, \; -714),\; {\rm Z}(574, \; -645)\] It can be verified that triangle \(\rm ABC\) contains the origin..
A number chain is created by continuously adding the square of the digits in a number to form a new number until it has been seen before For example, 44 → 32 → 13 → 10 → 1 → 1 85 → 89 → 145 → 42 → 20 → 4 → 16 → 37 → 58 → 89 Therefore any chain that arrives at 1 or 89 will become stuck in an endless loop. What is most amazing is that EVERY starting number will eventually arrive at 1 or 89. How ma..
It is well known that if the square root of a natural number is not an integer, then it is irrational. The decimal expansion of such square roots is infinite without any repeating pattern at all. The square root of two is 1.41421356237309504880..., and the digital sum of the first one hundred decimal digits is 475. For the first one hundred natural numbers, find the total of the digital sums of ..