Question

The numbers , 1, 2, 3, 1984 and 1985 are written on a blackboard .

We decide to erase from the blackboard , any two numbers and replace them with their positive difference .

After this is done several times , a single number remains on the blackboard .

Can this number equal 0 ? ​

Answer 1

Answer:-

0 can never be the single number which appears finally.

Reason:-

We can see that the three numbers among the five, written on the blackboard, are odd numbers and the other two are even numbers. $\quad$

We must know that,

• Difference between two odd numbers is always an even number.

• Difference between two even numbers is always an even number.

• Difference between an odd number and an even number is always an odd number.

So if we take the difference of the five numbers in the blackboard to get a single number in any possible way, we always get an odd number.

odd - odd - odd - even - even = odd

even - even - odd - odd - odd = odd

But, unfortunately, 0 is not an odd number.

Hence 0 can't be the single number.

Answer 2

Answer:

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