Problem C. 1133. (September 2012)

C. 1133. The digits of the sixth power of a natural number in ascending order are as follows: 0, 2, 3, 4, 4, 7, 8, 8, 9. Which number is it?

(5 pont)

Deadline expired on October 10, 2012.

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

Megoldás. Az adott számjegyekből összeállítható legkisebb hatjegyű szám a 203447889, a legnagyobb pedig a 988744320. Ez alapján:

203447889 $\leq$ a⁶ $\leq$ 988744320.

Mindkét oldalból 6-dik gyököt vonva:

24,25 $\leq$ a $\leq$ 31,56,

vagyis

25 $\leq$ a $\leq$ 31.

Mivel a számjegyek összege osztható 3-mal, ezért a is 3-mal osztható. Így a 27 vagy 30 lehet, ebből csak a 27 jó.

Statistics:

485 students sent a solution.

5 points: 415 students.

4 points: 48 students.

3 points: 7 students.

2 points: 6 students.

1 point: 8 students.

Unfair, not evaluated: 1 solutions.

Problems in Mathematics of KöMaL, September 2012

485 students sent a solution.
5 points:	415 students.
4 points:	48 students.
3 points:	7 students.
2 points:	6 students.
1 point:	8 students.
Unfair, not evaluated:	1 solutions.

Already signed up?
New to KöMaL?