What is the remainder on dividing the sum 2 + 2 squared + 2 cubed + ... + 2 to the power 10 by 10?

The empty squares below are to be filled by writing numbers: 1, blank, blank, blank, blank, 6 (six squares in a row). The sum of the numbers in any three consecutive squares must be 10. What number should be written on the second square?

Between 1 and 100, how many numbers are there with exactly three factors?

What is the decimal form of the sum 1/5 + 1/5 squared + 1/5 cubed + 1/5 to the power 4?

On dividing each of 12 and 23 by a number greater than 1, we get the same remainder. What is the remainder?