On Monday, Jessica told two friends a secret. On Tuesday, each of those friends told the secret to two other friends. Each time a student heard the secret, he or she told the secret to two other friends the following day. On what day of the week will 1023 students know the secret?
+26367 On Monday, Jessica told two friends a secret. On Tuesday, each of those friends told the secret to two other friends. Each time a student heard the secret, he or she told the secret to two other friends the following day. On what day of the week will 1023 students know the secret?
\(\begin{array}{|r|r|l|} \hline \text{day of the week} & & \text{sum} \\ \hline \text{Jessica} & 1 = 2^0 & 1\\ \text{Monday} & 2 = 2^1 & 2^2-1 = 3 \\ \text{Tuesday} & 2*2 = 2^2 & 2^3-1 = 7 \\ \text{Wednesday}& = 2^3 & 2^4-1 = 15 \\ \text{Thursday} & = 2^4 & 2^5-1 = 31 \\ \text{Friday} & = 2^5 & 2^6-1 = 63 \\ \text{Saturday} & = 2^6 & 2^7-1 = 127 \\ \text{Sunday} & = 2^7 & 2^8-1 = 255 \\ \text{Monday} & = 2^8 & 2^9-1 = 511 \\ \color{red}\text{Tuesday} & = 2^9 & 2^{10}-1 = 1023 \\ \hline \end{array} \)
