## Task 1 - 250711

In a bag, there is $1 \mathrm{~kg}$ of sugar. Using a balance scale with two weighing pans (each large enough for $1 \mathrm{~kg}$ of loose sugar) and exactly one $50 \mathrm{~g}$ weight, $300 \mathrm{~g}$ of sugar should be weighed out.

Show that this is possible with only three weighings!
First, one halves the kilogram of sugar without weights and obtains two 500 g portions. In the same way, one halves the 500 g of sugar and obtains two 250 g portions. With the help of the 50 g weight, one determines 50 g of sugar and adds it to the 250 g. Thus, one has 300 g of sugar.

Another solution:

With the 50 g weight, one determines 50 g of sugar. With these 50 g and the 50 g weight, one determines (from the remaining sugar) 100 g of sugar in a second weighing, which together with the 50 g of sugar results in 150 g of sugar.

With these 150 g of sugar, one determines another 150 g of sugar, so that the contents of the two scales together amount to 300 g of sugar.