Real Mathematics – Game #4

The Last Biscuit

I think I was making use of my hunter-gatherer genes when I was a child.

I admit it; I’ve always loved junk food and it was a big problem in my childhood since we had a big family. And on top of that I was among the youngest children in that crowd which meant I had a physical disadvantage against other kids about matters such as getting to eat Pringles first. Also, almost everyone around me was competitive which made it harder for me to get junk food.

In the end my hunter-gatherer genes helped me. Although I wish I was craftier so that I could have created games which only I’d win.

Tea Party

Tea is almost there, biscuits are ready and willing. I am warming up my wrist so that when I dunk my biscuits into my tea I will have enough agility to save the biscuit from getting crumbled into my tea cup. Oh boy! Someone at the door… Now I have a guest!

I have two kinds of biscuits: Cacao and regular. I love the ones with cacao more than the regular ones. Well, who doesn’t?! The problem is that I only have four cacao biscuits along with six regular ones. Neither my friend nor I can decide who will get the cacao biscuits. We could share, but there is no fun in it! That is why we let a game decide our faiths.



  • Each player will take turn.
  • In each turn a player could either take any number of biscuits from just one stack or take the same amount from both stacks.
  • The player who takes the last biscuit(s) is the winner.

Example: Host vs. Guest

There are six regular and four cacao biscuits in stacks.

Guest starts first and takes one from cacao.

Host takes one from regular. In second turn guest takes one from each stacks.

Host takes three from regular biscuits.


Guest takes one from cacao.


Now there is one from each biscuits and host takes them both to claim his/her victory.

One wonders…

  1. Does it matter who goes first in the host vs. guest example?
  2. When did you understand that the guest lost? Would it change anything if guest played his/her move differently in the final turn?
  3. Can you find a method that makes you the winner if you play this game with different numbers of biscuits?

M. Serkan Kalaycıoğlu



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