---
id: 5900f38d1000cf542c50fea0
title: 问题33:数字取消分数
challengeType: 5
videoUrl: ''
dashedName: problem-33-digit-cancelling-fractions
---
# --description--
分数九十八分之四十九是好奇馏分,如在试图简化它可能会错误地认为九十八分之四十九 = 4/8,这是正确的,则通过取消787-9获得一个没有经验的数学家。我们应考虑馏分喜欢, 五十○分之三十○= 3/5,是微不足道的例子。这种类型的分数恰好有四个非平凡的例子,小于一个值,并且在分子和分母中包含两个数字。如果这四个分数的乘积以其最低公共项给出,请找到分母的值。
# --hints--
`digitCancellingFractions()`应该返回100。
```js
assert.strictEqual(digitCancellingFractions(), 100);
```
# --seed--
## --seed-contents--
```js
function digitCancellingFractions() {
return true;
}
digitCancellingFractions();
```
# --solutions--
```js
function digitCancellingFractions() {
function isCurious(numerator, denominator) {
const fraction = numerator / denominator;
const numString = numerator.toString();
const denString = denominator.toString();
if (numString[1] === '0' && denString[1] === '0') {
// trivial
return false;
}
for (let i = 0; i < 2; i++) {
for (let j = 0; j < 2; j++) {
if (numString[i] === denString[j]) {
const newNum = parseInt(numString[1 - i], 10);
const newDen = parseInt(denString[1 - j], 10);
if (newNum / newDen === fraction) {
return true;
}
}
}
}
return false;
}
function findLargestDivisor(a, b) {
let gcd = a > b ? b : a;
while (gcd > 1) {
if (a % gcd === 0 && b % gcd === 0) {
return gcd;
}
gcd--;
}
return gcd;
}
function simplifyFraction(numerator, denominator) {
const divisor = findLargestDivisor(numerator, denominator);
return [numerator / divisor, denominator / divisor];
}
let multipleNumerator = 1;
let multipleDenominator = 1;
for (let denominator = 11; denominator < 100; denominator++) {
for (let numerator = 10; numerator < denominator; numerator++) {
if (isCurious(numerator, denominator)) {
multipleNumerator *= numerator;
multipleDenominator *= denominator;
}
}
}
return simplifyFraction(multipleNumerator, multipleDenominator)[1];
}
```