The Number That Describes Itself
Find the ten-digit number d₀d₁d₂…d₉ such that, for every i from 0 to 9, the digit dᵢ equals the number of times the digit i appears in the number itself. (For example, in 2020 in base 4, d₀ = 2 says there are two zeros, d₁ = 0 says no ones, and so on.) The number is unique. Give it as a ten-digit integer.
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Source: Self-describing numbers are a classic of recreational mathematics (discussed by Martin Gardner among others); this formulation written for AxiomIQ.