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Given:

Number of Days in a normal Year

To Do:

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

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  • $\begingroup$ Thx for the edit $\endgroup$ – Uvc May 18 at 11:00
  • $\begingroup$ you're welcome :) $\endgroup$ – Omega Krypton May 18 at 11:10
5
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First Way

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

Second Way

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

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2
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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.

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

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  • $\begingroup$ but it is a normal year... (ie 365 days) +1 tho! $\endgroup$ – Omega Krypton May 18 at 14:15
  • $\begingroup$ @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! $\endgroup$ – Weather Vane May 18 at 14:20
  • $\begingroup$ true, mathsisfun.com/definitions/year.html lol $\endgroup$ – Omega Krypton May 18 at 14:23
  • $\begingroup$ 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 $\endgroup$ – Uvc May 18 at 14:41

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