Question

The sum of the digits of a n-digit positive integer is 20. What is the maximum possible product of the n digits?

Answer 1

Answer:

Step-by-step explanation: 2n≤n2 for n≥2 and 2n+1<n(n+1) for n≥2. So we do not need to use any number bigger than 3 to get the maximum value. Clearly there is no benefit in using 1s. We have 32>23, so it is better to use 3s rather than 2s. The largest number available is six 3s which takes us up to 18. Hence the maximum is 2⋅36=1458.