Question

The numbers 1 through 10 are written on a board. You can erase any two numbers and replace them with their difference. Is it possible to repeat this process until the only number on the board is 0?

Answer 1

That's right in the end we will get only zeros.

Explanation:

We can do a test:

-We choose two numbers for example 2 and 7; making the difference or subtraction would give a value of 5; Now when you start to make differences between two following numbers, it will give a value that will be repeated in double position, which will determine that at some point you will start to make differences in which the only value on the board is zero. .

1-2-3-4-5-6-7-8-9-10. We subtract and replace the value obtained in two positions.(7-2)=5;

Now we get:

1-5-3-4-5-6-5-8-9-10;

If we subtract 5 minus 5 we will obtain zero, and so we proceed to do the same with two following numbers, we replace the obtained value and then we make the difference between them.