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B. 4777. There are three species of creatures peopling the planet B-4777: the Alpha, the Beta and the Gamma. People of one species (not necessarily the Alpha) have 2 hands, people of another species have 3 hands, and people of the third species have 4 hands. People of one species (not necessarily those with 2 hands) have 4 fingers on each hand, people of another species have 5, and people of the third species have 6 hands on each hand. Every people represent numbers in a notation with a base equal to the total number of fingers on their hands. (For example, if those with 4 hands have 6 fingers on each, then they will use base-24 representation.) The number $\displaystyle 64_{\alpha}$ expressed in the notation of the Alpha people coincides with the number $\displaystyle 51_{\beta}$ expressed in the notation of the Beta people. How many hands and how many finger per hand do the Alpha, the Beta and the Gamma have?

Proposed by A. Sztranyák, Budapest

(3 points)

Deadline expired on 11 April 2016.

Statistics on problem B. 4777.
 160 students sent a solution. 3 points: 150 students. 2 points: 7 students. 1 point: 3 students.

• Problems in Mathematics of KöMaL, March 2016

•  Támogatóink: Morgan Stanley