2.8 KiB
2.8 KiB
id | challengeType | title |
---|---|---|
5900f38d1000cf542c50fea0 | 5 | Problem 33: Digit cancelling fractions |
Description
Instructions
Tests
tests:
- text: <code>digitCancellingFractions()</code> should return 100.
testString: assert.strictEqual(digitCancellingFractions(), 100, '<code>digitCancellingFractions()</code> should return 100.');
Challenge Seed
function digitCancellingFractions() {
// Good luck!
return true;
}
digitCancellingFractions();
Solution
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];
}