3.0 KiB
3.0 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f3971000cf542c50feaa | Problem 43: Sub-string divisibility | 5 | 302100 | problem-43-sub-string-divisibility |
--description--
The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it also has a rather interesting sub-string divisibility property.
Let d_1
be the 1^{st}
digit, d_2
be the 2^{nd}
digit, and so on. In this way, we note the following:
{d_2}{d_3}{d_4} = 406
is divisible by 2{d_3}{d_4}{d_5} = 063
is divisible by 3{d_4}{d_5}{d_6} = 635
is divisible by 5{d_5}{d_6}{d_7} = 357
is divisible by 7{d_6}{d_7}{d_8} = 572
is divisible by 11{d_7}{d_8}{d_9} = 728
is divisible by 13{d_8}{d_9}{d_{10}} = 289
is divisible by 17
Find the sum of all 0 to n
pandigital numbers with sub-strings fulfilling n - 2
of these divisibility properties.
Note: Pandigital numbers starting with 0
are to be considered in the result.
--hints--
substringDivisibility(5)
should return a number.
assert(typeof substringDivisibility(5) === 'number');
substringDivisibility(5)
should return 12444480
.
assert.strictEqual(substringDivisibility(5), 12444480)
substringDivisibility(7)
should return 1099210170
.
assert.strictEqual(substringDivisibility(7), 1099210170)
substringDivisibility(8)
should return 1113342912
.
assert.strictEqual(substringDivisibility(8), 1113342912)
substringDivisibility(9)
should return 16695334890
.
assert.strictEqual(substringDivisibility(9), 16695334890)
--seed--
--seed-contents--
function substringDivisibility(n) {
return true;
}
substringDivisibility(5);
--solutions--
function substringDivisibility(n) {
function isSubDivisable(digits) {
const factors = [2, 3, 5, 7, 11, 13, 17];
for (let i = 1; i < digits.length - 2; i++) {
const subNumber = digits[i] * 100 + digits[i + 1] * 10 + digits[i + 2];
if (subNumber % factors[i - 1] !== 0) {
return false;
}
}
return true;
}
function heapsPermutations(k, digits, conditionCheck, results) {
if (k === 1) {
if (conditionCheck(digits)) {
const number = parseInt(digits.join(''), 10);
results.push(number);
}
return;
}
heapsPermutations(k - 1, digits, conditionCheck, results);
for (let i = 0; i < k - 1; i++) {
if (k % 2 === 0) {
[digits[i], digits[k - 1]] = [digits[k - 1], digits[i]];
} else {
[digits[0], digits[k - 1]] = [digits[k - 1], digits[0]];
}
heapsPermutations(k - 1, digits, conditionCheck, results);
}
return;
}
const allowedDigits = [...new Array(n + 1).keys()];
const divisablePandigitals = [];
heapsPermutations(
allowedDigits.length,
allowedDigits,
isSubDivisable,
divisablePandigitals
);
let sum = 0;
for (let i = 0; i < divisablePandigitals.length; i++) {
sum += divisablePandigitals[i];
}
return sum;
}