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IMSO 2014 — Math Division — Exploration Question 2

IMSO Maths · IMSO 2014 — Math Division — Exploration

Question 2

In the Indonesian village Sevenia, each bill is worth a number of rupiahs equal to a power of $7$, namely, $7^0=1$, $7^2=49$, $7^3=343$, $7^4=2401$, $7^5=16807$, $7^6=117649$, $7^7=823543$ and so on. A millionaire has some bills worth a total of exactly $1000000$ rupiahs, but at most $8$ bills of any kind. No two millionaires have exactly the same combination of bills. What is the maximum number of millionaires in Sevenia?