3. The king summoned two male wizards to the palace. He asked Wizard A to first write down 100 positive real numbers (allowing duplicates) on a card, without revealing them to Wizard B. Then, B must accurately write down all 100 positive real numbers, or both wizards will be beheaded. A is allowed to provide B with a list of numbers, each of which is either one of the 100 positive real numbers or the sum of several of these 100 positive real numbers, but he cannot tell B which are the numbers on the card and which are the sums of the numbers on the card. In the end, the king decided to pull out the same number of whiskers from each wizard based on the number of numbers in the list. Given that the two wizards cannot communicate beforehand, how many whiskers at least need to be pulled out to ensure they do not lose their lives?
3. 101 roots.

A provides a sequence of numbers $1,2,4, \cdots, 2^{99}$, whose sum is $2^{100}-1$. Thus, B understands that the number on the card is no more than 1, hence there is another number no more than $2, \cdots \cdots$ eventually the number on the 100th card is no more than $2^{99}$. Therefore, their sum does not exceed $2^{100}-1$ and equality holds if and only if these 100 numbers are $1,2,4, \cdots, 2^{99}$.