Mathematical and Physical Journal
for High Schools
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Problem C. 880. (January 2007)

C. 880. Which six-digit number will be multiplied by three if its first digit is reduced by three and a digit of three is attached to the end?

(5 pont)

Deadline expired on February 15, 2007.


Sorry, the solution is available only in Hungarian. Google translation

Megoldás: A keresett hatjegyű számot írjuk 100\,000a+b alakban, ahol a=3, 4, 5, 6, 7, 8, 9, a b pedig ötjegyű egész szám. A szöveg szerint:

3(100\,000a+b)=1\,000\,000(a-3)+10b+3,

0=700\,000a+7b-2\,999\,997,

b=\frac{2\,999\,997-700\,000a}{7}.

Csak az a=4 esetén kapnuk b-re ötjegyű pozitív egész számot: b=28\,571. Vagyis a keresett szám: 428\,571.

Valóban 428\,571\cdot3=1\,285\,713.


Statistics:

437 students sent a solution.
5 points:415 students.
4 points:3 students.
3 points:1 student.
2 points:2 students.
1 point:5 students.
0 point:5 students.
Unfair, not evaluated:6 solutions.

Problems in Mathematics of KöMaL, January 2007