1.4 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f4231000cf542c50ff36 | Problem 183: Maximum product of parts | 5 | 301819 | problem-183-maximum-product-of-parts |
--description--
Let N
be a positive integer and let N
be split into k
equal parts, r = \frac{N}{k}
, so that N = r + r + \cdots + r
.
Let P
be the product of these parts, P = r × r × \cdots × r = r^k
.
For example, if 11 is split into five equal parts, 11 = 2.2 + 2.2 + 2.2 + 2.2 + 2.2, then P = {2.2}^5 = 51.53632
.
Let M(N) = P_{max}
for a given value of N
.
It turns out that the maximum for N = 11
is found by splitting eleven into four equal parts which leads to P_{max} = {(\frac{11}{4})}^4
; that is, M(11) = \frac{14641}{256} = 57.19140625
, which is a terminating decimal.
However, for N = 8
the maximum is achieved by splitting it into three equal parts, so M(8) = \frac{512}{27}
, which is a non-terminating decimal.
Let D(N) = N
if M(N)
is a non-terminating decimal and D(N) = -N
if M(N)
is a terminating decimal.
For example, \sum D(N)
for 5 ≤ N ≤ 100
is 2438.
Find \sum D(N)
for 5 ≤ N ≤ 10000
.
--hints--
maximumProductOfParts()
should return 48861552
.
assert.strictEqual(maximumProductOfParts(), 48861552);
--seed--
--seed-contents--
function maximumProductOfParts() {
return true;
}
maximumProductOfParts();
--solutions--
// solution required