# Number of Days in a Year with Consecutive Perfect Squares

Given:

Number of Days in a normal Year

To Do:

Express it in two different ways utilizing Squares of consecutive positive numbers.

• Thx for the edit – Uvc May 18 at 11:00
• you're welcome :) – Omega Krypton May 18 at 11:10

First Way

$$13^2+14^2=169+196=365$$

Second Way

$$10^2+11^2+12^2=100+121+144=365$$

Also

In a leap year (normally every 4th year)

$$8^2 + 9^2 + 10^2 + 11^2 = 64 + 81 + 100 + 121 = 366$$

And

In 1752 (a leap year but definitely abnormal) 11 days were removed from the calendar, so there were only 355 days.

$$5^2 + 6^2 + 7^2 + 8^2 + 9^2 + 10^2 = 25 + 36 + 49 + 64 + 81 + 100 = 355$$

• but it is a normal year... (ie 365 days) +1 tho! – Omega Krypton May 18 at 14:15
• @OmegaKrypton the question did ask for a "normal" year, and I tried in the first part to get round that because a leap year is normal, except for 2100 etc. In the second part I have no excuse – I just wanted to post the discovery! – Weather Vane May 18 at 14:20
• – Omega Krypton May 18 at 14:23
• Puzzles need to be enjoyed ...not dissected..good extraneous info..normal is most of the time..if you ask normal person he would say what most people would expect – Uvc May 18 at 14:41