Problem K. 454. (February 2015)

K. 454. Several digits of the numbers in the operations below have been replaced with letters. Different letters stand for different digits, and identical letters stand for identical digits. No letter denotes the digit 1.

\(\displaystyle 1 \cdot \mathrm{G} + 1 = \mathrm{H}, \)

\(\displaystyle 1\mathrm{A} \cdot \mathrm{G} + 2 = \mathrm{HG}, \)

\(\displaystyle 1\mathrm{AB} \cdot \mathrm{G} + 3 = \mathrm{HGF}, \)

\(\displaystyle 1\mathrm{ABC} \cdot \mathrm{G} + 4 = \mathrm{HGFE}, \)

\(\displaystyle 1\mathrm{ABCD} \cdot \mathrm{G} + 5 = \mathrm{HGFED}.\)

Find the value of each letter.

(6 pont)

Deadline expired on March 10, 2015.

Statistics:

50 students sent a solution.
6 points:	Agócs Katinka, Braun Dániel, Csuha Boglárka, Dömötör Emőke, Encz Koppány, Farkas Lilla, Fekete Balázs Attila, Harsányi Benedek, Hegedűs 330 Marcell, János Zsuzsa Anna, Járomi Bence, Korpás Isabel, Kozma Dávid Márk, Márton Anna, Mihályházi Péter, Nagy Marcell, Nagy Viktor, Németh Csilla Márta, Páhoki Tamás, Paulovics Péter, Pintér 345 Balázs, Rátkai Petra, Simon411 Máté, Sinkó Zsófia, Sipos Fanni Emma, Sisák László Sándor, Slenker Balázs, Szarka Álmos, Szilágyi Botond, Tamási Kristóf Áron, Tószegi Fanni, Valkó Bence, Varga 274 Tamás.
5 points:	Mészáros Melinda, Sántha 001 Balázs.
3 points:	3 students.
2 points:	3 students.
1 point:	4 students.
0 point:	5 students.

Problems in Mathematics of KöMaL, February 2015