Mathematical and Physical Journal
for High Schools
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Problem C. 1324. (December 2015)

C. 1324. Agnes is making gingerbread hearts for Christmas. The pastry cutter has the shape of a 6 cm by 6 cm square with two semicircles attached to two adjacent sides. She always rolls the dough the same thickness, forming a square whose side is a whole number of decimetres. (If any dough remains, she gives it to her sister.) She starts cutting the hearts out of the pastry by placing the corner of the cutter to the corner of the pastry square, carefully aligning the sides. Then she continues by placing the cutter next to the cut-out squares with the same orientation, as close as possible. How many squares can Agnes make if she starts out with a 1 m\(\displaystyle {}^2\) pastry, and she always kneads together the pastry remaining after cutting out the hearts?

(5 pont)

Deadline expired on January 11, 2016.


188 students sent a solution.
5 points:128 students.
4 points:9 students.
3 points:11 students.
2 points:18 students.
1 point:11 students.
0 point:9 students.
Unfair, not evaluated:2 solutions.

Problems in Mathematics of KöMaL, December 2015