Problem B. 4526. (March 2013)

B. 4526. A wildfire spreads at a speed of 1 km/h in all directions. When the fire has burnt a circle of radius 1 km, an excavator arrives at the edge of the fire to dig a ditch to stop the spreading of the fire. The excavator can proceed at a maximum speed of 14 km/h. Find a possible path for the excavator such that the fire should not burn a total area greater than 13 km².

Quantum

(4 pont)

Deadline expired on April 10, 2013.

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

Megoldás. Egy lehetséges megoldás a következő: A bulldózer először távolodjon 1 km-t, majd ásson árkot egy 2 km. sugarú kör mentén. Ehhez összesen 1+4 $\pi$ $\approx$ 13,57<14 kilométert kell megtennie, tehát a kör alakú árkot elkészítheti kevesebb, mint 1 óra alatt. Ezalatt a tűz nem éri el a 2 kilométer sugarú kört.

A kör belsejének területe 2² $\pi$ $\approx$ 12,57<13 km².

Statistics:

115 students sent a solution.

4 points: 90 students.

3 points: 8 students.

2 points: 10 students.

1 point: 2 students.

0 point: 2 students.

Unfair, not evaluated: 3 solutionss.

Problems in Mathematics of KöMaL, March 2013

115 students sent a solution.
4 points:	90 students.
3 points:	8 students.
2 points:	10 students.
1 point:	2 students.
0 point:	2 students.
Unfair, not evaluated:	3 solutionss.

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