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 solutionss.

Problems in Mathematics of KöMaL, January 2007

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 solutionss.

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