# Driplets

You might like to have a go at the game Last Bead before this one.

This is a game for two players.

Take turns to remove as many driplets as you like from a single driplet trail. Click once to choose, and once again in the same place to confirm.

The winner is the person to take the very last drip or drips.

Below you can play against Al, our computer, but you can also play offline against a friend using coins or counters arranged in heaps instead of drips arranged on drip trails.

Press 'New Game' to start, you then have 20 seconds to make the first move before Al, the computer, loses patience and starts anyway.

Can you find a winning strategy?

Hint: Count the drip trails with single drips and those with two drips: are those numbers even or odd?  How might this help you find a strategy? You can also watch Rachel and Marianne play the game to see how they got on.

Mastered this game? Then why not try Droplets or, for a challenge, Drips?

### Maths

The first player always wins.

### Interesting thought Jenil!

Interesting thought Jenil! Can you explain why?

### SO HARD

Its so hard. I have never won

I agree

### Strategy

All you have to do is...

If there is an odd number of beads, go first. If there is an even number, let Al go first because if there are 3 beads, you take, then AL takes then you take the last one. Whereas with 4, AL goes, then you go, then AL goes, then you go again and take the last one.

### Hi Toby! Good approach! But

Hi Toby! Good approach! But what if AL takes two beads in one go? Does the strategy still work?

### maths

If it is a even number then let al go first, if it still is an even number you make it even.

### Thanks Raphaela! Can you

Thanks Raphaela! Can you explain what you need there to be an "even number" of?

### The strategy is this

The Strategy is if you go on an uneven number you will win

### Re: The strategy is this

Can you explain a little more? Perhaps you could use some examples to help?

### diplits

once you have got two sets of two things do the same thing as the computer

### droplets

First I count the drop trails to see if there is a odd number and try to have a go but usually I leave my opponent to go first. Then if I should have taken a drop, I take one drop and if my opponent does that I take another.

### droplets

So what do you do if there is an even number of drop trails?

Would it be more useful to consider which types of trails are odd or even? After all, the trails come either as a single drop or as a pair of drops.

### Driplets Solution

Here is the solution my students came up with for Driplets!

If there are an even number of single drops and an odd number of pairs of drops; kill one pair of drops then mimic Al.

If the sets of single and pairs of drops are both even, then let Al go first and mimic Al after that.

If there are an even number of pairs of drops and an odd number of single drops, you take away one single drop and then mimic Al.

If there is an odd number of the single drops and the pairs of drops, then take away one bottom of a pair to make the singles and pairs even, then mimic Al.

### Driplets Solution

That's an excellent strategy that makes sure to consider each possibility.

You might want to show your students Droplets and see how to adapt that strategy to solve that problem. Afterwards, you may also like to look at Drips which extends the problem even further.