Kazitsyna T.

Baba Yaga was given large sandglasses for 5 minutes and small ones for 2 minutes. The potion must boil continuously for exactly 8 minutes. When it started boiling, all the sand in the large sandglasses was in the lower half, and in the small sandglasses, some (unknown) part of the sand was in the upper half, and the rest was in the lower half. Help Baba Yaga measure exactly 8 minutes.

(The sand keeps flowing at a constant rate. No time is spent on flipping the sandglasses.)

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Let at the beginning in the upper half of the small hourglass there was sand for $x$ minutes.
![](https://cdn.mathpix.com/cropped/2024_05_06_f579c76dfb5bc127b163g-21.jpg?height=780&width=1096&top_left_y=919&top_left_x=480)

From the start of the process, $x+x+(2-x)+(2-x)=4$ minutes have passed, and the sand in both hourglasses is entirely in the lower half. It remains to measure 4 minutes - this can easily be done using the 2-minute hourglasses.

The solution is not unique. However, it can be shown that in any solution, it is necessary to immediately start the large hourglasses.