Project Euler/28 - Revision history

Unknown user: /* Sum of Diagonals for 1001×1001 Spiral */

2025-04-19T00:45:37Z

Sum of Diagonals for 1001×1001 Spiral

← Older revision		Revision as of 00:45, 19 April 2025
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	<math>16 \cdot 41791750 + 4 \cdot 125250 + 4 \cdot 500 = 669171000</math>		<math>16 \cdot 41791750 + 4 \cdot 125250 + 4 \cdot 500 = 669171000</math>

	Add the center: <math>669171000 + 1 = ~~669171001~~</math>.		Add the center: <math>669171000 + 1 = \mbox{the final answer}</math>.

	=== Algorithm to Compute the Sum ===		=== Algorithm to Compute the Sum ===

Unknown user: /* Corner Numbers on Diagonals */

2025-04-19T00:45:05Z

Corner Numbers on Diagonals

← Older revision		Revision as of 00:45, 19 April 2025
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	Verify for <math>5 \times 5</math> (<math>k = 2</math>):		Verify for <math>5 \times 5</math> (<math>k = 2</math>):
	* Layer 1 (<math>m = 1</math>):		* Layer 1 (<math>m = 1</math>):
	** Top-right: <math>(2 \times 1 + 1)^2 = 9</math>		** Top-right: <math>(2 \times 1 + 1)^2 = 9</math>
	** Top-left: <math>9 - 2 \times 1 = 7</math>		** Top-left: <math>9 - 2 \times 1 = 7</math>
	** Bottom-left: <math>9 - 4 \times 1 = 5</math>		** Bottom-left: <math>9 - 4 \times 1 = 5</math>
	** Bottom-right: <math>9 - 6 \times 1 = 3</math>		** Bottom-right: <math>9 - 6 \times 1 = 3</math>
	* Layer 2 (<math>m = 2</math>):		* Layer 2 (<math>m = 2</math>):
	** Top-right: <math>(2 \times 2 + 1)^2 = 25</math>		** Top-right: <math>(2 \times 2 + 1)^2 = 25</math>
	** Top-left: <math>25 - 2 \times 2 = 21</math>		** Top-left: <math>25 - 2 \times 2 = 21</math>
	** Bottom-left: <math>25 - 4 \times 2 = 17</math>		** Bottom-left: <math>25 - 4 \times 2 = 17</math>
	** Bottom-right: <math>25 - 6 \times 2 = 13</math>		** Bottom-right: <math>25 - 6 \times 2 = 13</math>

	These match the grid.		These match the grid.

Unknown user at 00:43, 19 April 2025

2025-04-19T00:43:17Z

Show changes

Unknown user at 00:41, 19 April 2025

2025-04-19T00:41:14Z

@@ Line 1: / Line 1: @@
 <pre>
 function sumDiagonals(n):
@@ Line 11: / Line 120: @@
 print(result)
 </pre>

Unknown user: Created page with "

 function sumDiagonals(n):     k = (n - 1) / 2     sum = 1  # Center     for m from 1 to k:         sum += 16 * m * m + 4 * m + 4     return sum  n = 1001 result = sumDia..."

2025-04-19T00:39:14Z

Created page with "<pre> function sumDiagonals(n): k = (n - 1) / 2 sum = 1 # Center for m from 1 to k: sum += 16 * m * m + 4 * m + 4 return sum n = 1001 result = sumDia..."

New page

<pre>
function sumDiagonals(n):
k = (n - 1) / 2
sum = 1 # Center
for m from 1 to k:
sum += 16 * m * m + 4 * m + 4
return sum

n = 1001
result = sumDiagonals(n)
print(result)
</pre>