Question

Imagine that we have 49 cards with the values written on their faces, (they are all visible ) as follows; 25, 24, 23, 22, ........3, 2, 1, 2, 3, .........23, 24, 25 Now, suppose Paola and Victor are choosing cards from this line sequentially. Paola is making the first choice and Victor is following her and they continue sequentially. Notice that they can choose the card from any position. Show that Paola has a simple strategy which guarantees exactly a sum (sum of the values written on the faces of the cards she collects) equals to that of Victor plus one.

Answer 1

There is a simple strategy here for each one .took the highest number card possible . Because there are only 49 cards means one person ,who is picking first will choose one extra card from other one.so paola will choose another card.

So paola moving first ,she will pick 25 number ,then vickor also picks 25 number as there are two 25 number cards.

Then paola picks 24 number card and vickor too pick 24 number card.

And this process will continue till when at atlast paola picks number 2 card and victo too picks number too card.

So far ,there are two cards available for each number one is picked by paola and second one is picked by vickor ,so both have same sum.

Now there is only one card left ,number 1 card and the picking move is of paola,so he picks card with number 1 and game end.

At game ends ,paola sum is exactly plus one than vickor.