# This king needs therapy if he wants to make new weights which can measure 10^100

**Number Theory**Level 5

King Mathematica of the shining empire of Scientia has had a brainwave. He wishes to remove imperial and standard units of mass out of his empire. Instead, he will create a new type of unit for mass. He calls it *margs*. He wants to create models for each weight using pure gold, but wants to use as less models as possible but has to have all weights with a model.

Now, this kingdom is not very sophisticated and has no weighing machine but it does have balancing scales. When the king manufactures the new weights (out of lead, of course), he wants to create as less weight types as possible. If he made only a 1 marg weght and a 4 marg weight, then people would be only able to weight 1 marg, 4 margs, 3 margs (by putting a weight on either side of a balancing scale) and 5 margs.

The king asks you, his wise man to tell him what the minimum number of models he needs to make to weigh all weights from 1 to \(10^{100}\) margs. You think and reply to him correctly. What did you say?

**Your answer seems reasonable.**Find out if you're right!

**That seems reasonable.**Find out if you're right!

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