Question 1151144
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The 5 numbers that meet the description are <font color="blue">442, 445, 481, 485, 493</font>


Based on what is shown below:
1^2 + 21^2 = 1 + 441 = <font color="blue">442</font>
9^2 + 19^2 = 81 + 361 = <font color="blue">442</font>
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2^2 + 21^2 = 4 + 441 = <font color="blue">445</font>
11^2 + 18^2 = 121 + 324 = <font color="blue">445</font>
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9^2 + 20^2 = 81 + 400 = <font color="blue">481</font>
15^2 + 16^2 = 225 + 256 = <font color="blue">481</font>
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1^2 + 22^2 = 1 + 484 = <font color="blue">485</font>
14^2 + 17^2 = 196 + 289 = <font color="blue">485</font>
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3^2 + 22^2 = 9 + 484 = <font color="blue">493</font>
13^2 + 18^2 = 169 + 324 = <font color="blue">493</font>
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I used a perl script to search for all the integers between 440 and 500, excluding the endpoints (see note below), such that the integer could be broken down into a sum of two distinct squares.


Note: we can express 500 as a sum of two different squares in two different ways
4^2 + 22^2 = 16 + 484 = 500
10^2 + 20^2 = 100 + 400 = 500
but that would mean we're dealing with 6 values instead of 5. So it appears we are ignoring the endpoints 440 and 500. 


We are also ignoring 450
3^2 + 21^2 = 9+441 = 450
15^2 + 15^2 = 225+225 = 450
because the second summation line has us adding the same square to itself, ie we dont have two distinct square numbers here. 


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Once again the five numbers are: <font color="blue">442, 445, 481, 485, 493</font>


The median is the middle most value. In this case, it would be the value in the third slot.


Answer: <font color=red size=4>481</font>
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