VTMO 2014 — Grade 6 — final

Distinct letters are distinct digits, $T = 3$, and $GET + THE = MATH$. Find $MATH$.

Teams $A$ and $B$ each have $10$ workers. A builds the road in $14$ days and bridge $25$; $B$ needs $18$ and $15$. Team $C$ combines $5$ from each and builds road then bridge. How many days are required? Assume equal, constant individual productivity within each team.

$A = 1 + 2^{2} + 2^{3} + \ldots + 2^{2014} + 2^{2015}$. Find A modulo $31$.

Vy travels at $5 \frac{\,\mathrm{km}}{h}$ on flat road, $4$ uphill, $6$ downhill. Outward travel takes $1 h = 36$ min, return $1 h = 39$ min. The flat part is $2.5$ km. Find total distance $VB$.

$A = 50$-page book with odd pages right and even pages left loses one two-page leaf. Remaining page numbers sum $1240$. Which two numbers were lost?