Question

Ramu and Kallu are playing a game of addition
and subtraction. They have written first 100
numbers side by side and they need to put
plus or minus signs in between and then final
results will be calculated. If the final sum comes
out to be an even number then Ramu will win
and if the sum comes out to be an odd number
then Kallu will win. Who will win the game?
Assume that both of them are playing smartly.​

Answer 1

Given :   Ramu and Kallu are playing a game of addition and subtraction. They have written first 100 numbers side by side and they need to put

plus or minus signs in between and then final results will be calculated.

If the final sum comes out to be an even number then Ramu will win

and if the sum comes out to be an odd number then Kallu will win.

To Find :  Who will win the game  

Solution:

Ramu will win the game  

Result will be an even number

1 to 100

There 50 even  numbers and 50 odd numbers

even numbers added or subtracted  together will always result in an even number    

odd numbers  added or subtracted    together will always result in an even number  

there are 50 odd numbers hence we can say there are 25  pairs of odd numbers

Each pair will result in an even number irrespective of sign  

Hence  we have only  left with even  numbers

So  final result will be an even number

Hence Ramu will win

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