Question

Find the number of zeroes in the product $1^1\times 2^2\times 3^3\times 4^4\times 5^5\times 6^6\times \cdots \times {49}^{49}$ ___

Answer 1

The fives will be less than the twos. Hence, we need to count only the fives.
Thus : $5^5\times {10}^{10}\times {15}^{15}\times {20}^{20}\times {25}^{25}\times {30}^{30}\times {35}^{35}\times {40}^{40}\times {45}^{45}$
gives us: 5+ 10+ 15 + 20 + 25 + 25 + 30 + 35 + 40 + 45 fives. Thus, the product has 250 zeroes.