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Last Biscuit

Biscuits
 

Can you win this game by taking the last biscuit?

Biscuits can be taken from the biscuit stacks in two ways:

  1. By taking any number from just one stack or
  2. By taking the same number from both stacks.

The winner is the person who takes the last biscuit/s.

Have a go playing against the computer using the interactive below. Play as many times as you like!

 

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Can you find a winning strategy? If so, can you describe it? (See here for some hints.) Share your thoughts and discoveries

If you'd like to play similar games, see Silver Dollar and Slippery Snail. Can you see the similarities?

Comments

Submitted by joe on Fri, 03/18/2016 - 11:37

you have to make them both even

Submitted by gmp26 on Thu, 05/05/2016 - 06:18

Are you sure?

If I leave 4,4 both piles are even and I will lose. So I think there's more to it than that.
Leaving the piles unbalanced is necessary for a win, but not sufficient. e.g. if you leave (10, 5) your opponent will win if they know what to do.

Submitted by emp1001 on Tue, 03/22/2016 - 10:21

Thanks for your comment, Joe. Can you explain why you think both piles need to have an even number of biscuits?

Submitted by Ellie B on Tue, 04/19/2016 - 17:15

This strategy is an easy strategy but it took me a while to figure it out. I come from South Hunsley Secondary School and my maths teacher introduced my class to this website.

Basically, you have to take an even amount from both sides or take some from one side but make sure that the computer can't take the rest by unbalancing the stacks of biscuits. E.g: 10 on both sides, take 5 from plain or chocolate so the computer can only take 5 from the other side and all the rest from the stack that you chose.

Submitted by mf344 on Fri, 06/17/2016 - 12:23

Thanks Ellie, that's really interesting! I have hidden your answers so hoers can choose whether they want to dee it or not.

Submitted by Unicorn on Fri, 01/13/2017 - 14:40

There's another strategy I'm from BFMS and I figured another out, you make so that you go first and you make them 1 up to 21 but they have to be even and you take away all of them.

Submitted by Milo and Keya on Tue, 06/21/2016 - 10:30

You have to make it so there are 2 biscuits on one side and one on the other. Ensure you do this before the computer!

Submitted by mf344 on Wed, 06/22/2016 - 10:39

Thanks Milo and Keya. Can you explain this further? What happens when you get to that position and how do you get there?

Submitted by natalie brushett on Tue, 06/28/2016 - 10:36

I recommend this game because if you play around you can find a way to win

Submitted by m kose on Tue, 06/28/2016 - 10:38

make the biscuits evan

Submitted by Anonymous on Fri, 07/01/2016 - 02:54

Make the biscuits even and go first take all biscuits you win

Submitted by Karolina on Thu, 08/04/2016 - 10:42

I realised that most of the time when i played the computer put me in a trap but i couldnt do vise versa-the trap was to leave one pile with 2 biscuits and the other with one,so start like that and go last!The computer will be in the trap and you automatically win! Also if you play with a friend put them in that trap and again you automatically win-just dont tell them this!!

Submitted by Mridul on Thu, 11/17/2016 - 09:40

Hi I'm Mridul my teacher at RVS told me to try all this.
My solution is take any equal number and go first. Eat all of them up. Simple!

Submitted by matthew on Thu, 03/02/2017 - 12:08

While that is true, how can you win the game if the biscuit piles aren't equal?