We will order the provinces by increasing population. The first and second provinces are not large, as for each of them, there will not be two provinces with a smaller population. In the third province, less than $14\%$ of the population lives, since in both provinces with a smaller population, the total is no more than $7\%+7\%$ $=14\%$. In the fourth province, less than $21\%$ of the population lives, as the population of any two smaller provinces is less than $7\%+14\%$ $=21\%$. For the same reasons, in the fifth province, less than $14\%+21\%$ $=35\%$ of the population lives. Therefore, in the first five provinces, less than $7\%+7\%+14\%+21\%+35\%$ $=84\%$ of the population lives. Consequently, there are more than 5 provinces.

Example of population distribution across six provinces: $7\%$, $7\%$, $11\%$, $16\%$, $25\%$, $34\%$ of the population.

## Answer

6 provinces.
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In the country of Distant, a province is called large if more than $7 \%$ of the country's population lives in it. It is known that for each large province, there are two provinces with a smaller population such that their combined population is greater than that of this large province. What is the smallest number of provinces that can be in the country of Distant?