Let b be the unknown base. When my son writes 253 in base b, this can be
interpreted as

2b^{2} + 5b + 3 = 136

or

2b^{2} + 5b - 133 = 0

or

(b - 7)(2b + 19) = 0

Since b is a whole, positive number, the only possible solution is 7;
the unknown base is 7.
Source: Berrondom, Marie
Categories: Number sense, Bases, Algebra
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