Sunday morning puzzle
I was led to this problem by my great friend Karthikβs son – Aadi – who is a whizkid in logic and numbers problems. I need to spend more time with him just to learn about more puzzles.
This problem was published in New York Times as the Tax Man Problem. I have changed the description a little – but the problem is the same.
You and I sit across a table with twelve cards marked 1 thru 12 between us. Following are the rules of the card:
1. You pick a card.
2. I get to pick all the factors of that card that are remaining on the table.
(To explain, if you picked card marked β10β first, I pick up β1β, β2β and β5β. )
3. We continue with this.
(To explain, now if you pick β8β, I pick β4β. Remember β1β and β2β are already gone in the previous move)
4. You CANNOT pick a card if there are no factors of that card left for me to pick.
(To continue with the above example, you cannot pick β11β now, because its only factor β1β is already gone and I am left with nothing to pick)
5. Finally, when you have run out moves (there is no card left for you to pick without violating Rule 4 OR there are no cards left on the table), the game is over.
6. Now we add up our cards.
Whoever has higher total, wins.
To finish off that example:
You: 10
I: 1,2,5
You: 8
I: 4
You: 12
I: 3,6
You: run out of moves (you cannot pick any of the remaining cards – 7,9,11 – since they have no factors left)
I: 7,9,11
Your total: 10 + 8 + 12 = 30
My total: 48 . I WIN!!
Question: What is the highest total you can get and win?