11 Plus Exams Forum

Stuck with this problem. Pls help
Robin & Susan are playing a game with 9 cards. The cards are numbered from 1 to 9. Robin & Susan take turns to pick up one card each. They keep all the cards they have picked. The winner is the first person who can make a total of 15 out of the cards in thier hands

Robin starts the game. After 2 turns each, Robin is holding the cards numbered 6 and 4, and Susan is holding cards numbered 2 and 5. It is Robin's turn to pick a card and he picks 8. Who do you think will win the game. Explain your answer carefully

My thoughts
Not sure what the answer is:
Robin could win the game if he can pick a 1 OR Susan can win the game if she picks a 1 and 7 next. So not sure what is the expected answer

Any help or pointing in the right direction greatly appreciated

Many thanks in advance

Susan cannot win the game on turn 6 as Rob has taken the 8 on turn 5. On turn 7 Rob can win if he takes 1 or 3. Regardless of what card Susan rakes on turn 6, Rob can win on turn 7.

Cards remaining are 1, 3, 7, 9

Susan has 2, 5. She can win if she picks 1 AND 7. She needs two turns to win.
Robin has 4, 6, 8. He will win when he picks any of the cards, 1 (6+8+1) or 3 (4+8+3) or 7 (8+7) or 9 (6+9).

Robin has 6,4 and 8. Susan has 2 and 5. Cards on the table are 1, 3, 7 and 9.

Susan will not make it to 15 in the current turn irrespective of whichever card she picks.

Robin will make it to 15 irrespective of whichever card he picks in his next turn ( e.g. 4+8+3, or 8+7, or 6+9,,,,)

Marcus de Sautoy, in the Royal Institution Christmas Lecture some years back, gave a very interesting way of looking at this problem:

Put the numbers 9 numbers into a magic number square.
Put an x over the numbers Robin takes.
Put an O over the numbers Susan takes.
It turns into a game of noughts and crosses.

Thanks one and all for very detailed explaination. Wonder what I would do without the kind support of this group.