A zero seems to be worth nothing. But placed in the middle of a number, it completely changes the value of its digits. Here the zero does not add: it shifts.
The Number with a Zero Inside
Riddle statement
Think of a two-digit number.
When a 0 is inserted between its two digits, the number becomes nine times larger.
What was the original number?
For example, if the number were 47, inserting a 0 in the middle would turn it into 407.
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Solution
Call the original number:
where $a$ is the tens digit and $b$ is the units digit.
After inserting a zero between the two digits, the number becomes:
The statement says that the new number is nine times the original:
Expanding:
Therefore:
or, simplifying:
Since $a$ and $b$ are digits, the possible solution is:
The original number was:
And inserting a zero gives:
Check:
Answer: the number was 45.