* feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
1.3 KiB
1.3 KiB
id, title, challengeType, videoUrl, dashedName
id | title | challengeType | videoUrl | dashedName |
---|---|---|---|---|
5900f3fc1000cf542c50ff0e | 问题143:研究三角形的Torricelli点 | 5 | problem-143-investigating-the-torricelli-point-of-a-triangle |
--description--
设ABC为三角形,所有内角均小于120度。设X为三角形内的任意点,并使XA = p,XC = q,XB = r。 Fermat挑战Torricelli找到X的位置,使p + q + r最小化。 Torricelli能够证明,如果在三角形ABC的每一侧构造等边三角形AOB,BNC和AMC,则AOB,BNC和AMC的外接圆将在三角形内的单个点T处相交。此外,他证明了T,称为Torricelli / Fermat点,最小化p + q + r。更值得注意的是,可以证明,当总和最小化时,AN = BM = CO = p + q + r,并且AN,BM和CO也在T处相交。
如果总和最小化并且a,b,c,p,q和r都是正整数,我们将称三角形ABC为Torricelli三角形。例如,a = 399,b = 455,c = 511是Torricelli三角形的示例,其中p + q + r = 784.找到Torricelli三角形的p + q +r≤120000的所有不同值的总和。
--hints--
euler143()
应返回30758397。
assert.strictEqual(euler143(), 30758397);
--seed--
--seed-contents--
function euler143() {
return true;
}
euler143();
--solutions--
// solution required