The Vellum Skin grants wishes, but after each wish, its area decreases: either by 1 dm² in the usual case, or by half - if the wish was a heartfelt one. Ten wishes reduced the area of the skin threefold, the next few - sevenfold, and after a few more wishes, the skin disappeared completely. What was the original area of the skin?

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Let the original area of the skin be $S$ dm² $(S>0)$. After the area was reduced threefold and then sevenfold, it became $S / 21$ dm². This number must be an integer; otherwise, it would be impossible to get 0 by dividing by 2 and subtracting 1.

Consider the first 10 wishes. Among them, there cannot be more than one ultimate wish, since after them, the area decreased threefold, and $S / 4 < S / 3$. Consider two cases.

1) There were no ultimate wishes. Then $S-10=S / 3$, so $S=15$. But this number is not divisible by 7, which contradicts the condition of the area being reduced sevenfold.
2) Suppose there were $k$ ordinary wishes first, then an ultimate wish, and then $9-k$ more ordinary wishes. Then $1 / 2(S-k)-(9-k)=S / 3$, from which $S=3(18-k)$. Considering that $k$ is an integer from 0 to 9, we find the only value of $k$ for which $S$ is divisible by 7: $k=4$. Therefore, $S=42$.

## Answer

42 dm².