**Problem:**

Let N be a positive integer and let N be split into k equal parts, r = N/k, so that N = r + r + ... + r.

Let P be the product of these parts, P = r [×] r [×] ... [×] r = rk.

For example, if 11 is split into five equal parts, 11 = 2.2 + 2.2 + 2.2 + 2.2 + 2.2, then P = 2.25 = 51.53632.

Let M(N) = Pmax 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 Pmax = (11/4)4; that is, M(11) = 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) = 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, ΣD(N) for 5 [≤] N [≤] 100 is 2438.

Find ΣD(N) for 5 [≤] N [≤] 10000.

Let P be the product of these parts, P = r [×] r [×] ... [×] r = rk.

For example, if 11 is split into five equal parts, 11 = 2.2 + 2.2 + 2.2 + 2.2 + 2.2, then P = 2.25 = 51.53632.

Let M(N) = Pmax 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 Pmax = (11/4)4; that is, M(11) = 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) = 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, ΣD(N) for 5 [≤] N [≤] 100 is 2438.

Find ΣD(N) for 5 [≤] N [≤] 10000.

**Solution:**

100

**Code:**

The solution may include methods that will be found here: Library.java .

The solution may include methods that will be found here: Library.java .

public interface EulerSolution{

public String run();

}

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