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?

Guest Feb 21, 2020

#2**+1 **

**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?**

\(\begin{array}{|r|r|l|} \hline \text{day of the week} & & \text{sum} \\ \hline \text{Jessica} & 1 = 2^0 & 1\\ \text{Monday} & 2 = 2^1 & 2^2-1 = 3 \\ \text{Tuesday} & 2*2 = 2^2 & 2^3-1 = 7 \\ \text{Wednesday}& = 2^3 & 2^4-1 = 15 \\ \text{Thursday} & = 2^4 & 2^5-1 = 31 \\ \text{Friday} & = 2^5 & 2^6-1 = 63 \\ \text{Saturday} & = 2^6 & 2^7-1 = 127 \\ \text{Sunday} & = 2^7 & 2^8-1 = 255 \\ \text{Monday} & = 2^8 & 2^9-1 = 511 \\ \color{red}\text{Tuesday} & = 2^9 & 2^{10}-1 = 1023 \\ \hline \end{array} \)

heureka Feb 21, 2020