Question

Find the smallest n for which the numbers 1², 2², 3², 4², ....n² can be split into two groups with the same sum.

A) 4
B) 5
C) 6
D) 7
E) 8
F) 9

Answer 1

To find the smallest n for which the numbers 1², 2², 3², 4², ....n² can be split into two groups with the same sum, follow these steps: calculate the sum of squared numbers, divide the sum by 2 to find the target sum for each group, solve for n by trying different values, and determine the smallest n that satisfies the equation.

Step-by-step explanation:

To find the smallest n for which the numbers 1², 2², 3², 4², ....n² can be split into two groups with the same sum, we need to determine the sum of all the squared numbers and divide it by 2. Let's break it down step by step.

1. Calculate the sum of squared numbers: 1² + 2² + 3² + 4² + ... + n² = n(n + 1)(2n + 1)/6.
2. Divide the sum by 2 to find the target sum for each group: n(n + 1)(2n + 1)/6 = 2 * target_sum.
3. Solve for n: n(n + 1)(2n + 1) = 12 * target_sum.
4. Try different values of n until we find the smallest one that satisfies the equation. The smallest n that satisfies the equation will be the answer.

By finding the smallest n, we can split the squared numbers into two groups with the same sum.