Question 799804
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Cannot be done.  The sum of two odd numbers is an even number, the sum of two even numbers is an even number and the sum of an odd number and and even number is an odd number.


Let *[tex \Large x_1] the first odd number in the range 1 to 20 and then *[tex \Large x_2,\,x_3,\,x_4,\,x_5] be the other four odd numbers.


Regardless of the actual value of *[tex \Large x_1] and *[tex \Large x_2], the sum *[tex \Large x_1\ +\ x_2] must be even since both of the addends are odd.


Likewise *[tex \Large x_3\ +\ x_4] must also be even, and furthermore *[tex \Large (x_1\ +\ x_2)\ +\ (x_3\ +\ x_4)] must then be even because both addends are even.


Then, since the sum of the first four is necessarily even, adding the fifth odd number makes the grand total an odd number.  But 50 is an even number, hence no solution.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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