Final answer:
The two-digit number is 55, where both the tens and ones digits are the same and when the digit (5) is doubled, it results in 10.
Step-by-step explanation:
The question involves a simple mathematical puzzle where we have to find a two-digit number such that both the tens and ones digits are the same and adding the digit twice results in ten. To solve this puzzle, we need to find the digit which, when added to itself (digit multiplied by 2), equals 10. This can be mathematically expressed as 2x = 10, where x is the digit we are looking for. Dividing both sides of the equation by 2, we find that x = 5. Hence, the two-digit number we are looking for, with the same digit in both the tens and ones place, is 55.