Question

Assume 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 Maria and Alex are choosing cards from this line sequentially. Maria is making the first choice and Alex is following her and they continue sequentially. Notice that they can choose the card from any position. Show that Maria 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 Alex plus one.

Answer 1

There's a easy strategy here for each having taken the highest possible number card. Since there are only 49 cards, one person can select one additional card from another.
So Maria moving first, she will select 25 cards, then Alex will also select 25 cards as there are two 25 cards.

Maria then picks 25 number card and Alex pick 25 number card too.

And this cycle will continue until atlast Maria selects number 2 card and Alex selects number 2 card too.

So far, for each number one is picked by Maria, and the second one is picked by Alex, so both have the same aggregate.

Now there's just one card remaining, number one card, and the step to pick is Maria, so he chooses the number one card and the end of the game.

At the end of the game, the number of Maria is only plus one than Alex.

So, Maria = Alex + 1

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