The sum of the numbers is 2 .
Hypatia's number is 1 and Euclid's number is also 1 and cubing a number 20 times is just taking it to the power of 60 so 1^60
=(1^10 )^6
=1^6 =1. Pythagoras's number is 2 and Ptolemy's number is −2 so cubing 2 twenty times is 2^60
=2^10⋅6
=(2^10 )^6
=1024^6 and cubing −2 twenty times is (−2) 60 =(−2) 10⋅6 =((−2)^10 )^6
=1024^6 ⋅(−1)^6
=(−1)⋅1024^6 =−1024^6
. Therefore, the sum of the numbers is 1+1+1024^6 − 1024^6 = 2 .
Question
euclid, pythagoras, ptolemy, and hypatia are playing a game where they all have to think of a number, and then cube that number 20 times. hypatia doesn't want to cube large numbers, so she chooses the number $1$. euclid thinks the same thing and also chooses the number $1$. however, pythagoras and ptolemy don't think ahead and pythagoras chooses $2$ and ptolemy chooses $-2$. after they finish cubing their numbers (pythagoras and ptolemy take a while), all four players write their final numbers on a piece of paper. what is the sum of the numbers they wrote on the piece of paper?