5

Part of 2017 AIME Problems

Problems(2)

Wot n' Base Representation

Source: 2017 AIME I #5

A rational number written in base eight is

\underline{a} \underline{b} . \underline{c} \underline{d}

, where all digits are nonzero. The same number in base twelve is

\underline{b} \underline{b} . \underline{b} \underline{a}

. Find the base-ten number

\underline{a} \underline{b} \underline{c}

Six Sums in Search of a Solver

Source: 2017 AIME II #5

A set contains four numbers. The six pairwise sums of distinct elements of the set, in no particular order, are

189

320

287

234

x

y

. Find the greatest possible value of

x+y