When the Three Billy Goats Gruff trip-trapped across the Troll’s bridge, what order did they cross in?

In what other order could they have crossed the bridge?

How many different answers can you find?

What if there were four goats in the story?

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# The Three Billy Goats Gruff

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25 thoughts on “The Three Billy Goats Gruff”

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There are many answers.

B-big goat

M- medium goat

S- small goat

B,m,s

B,s,m

M,s,b

M,b,s

S,m,b

S,b,m

That’s what I got from 3 goats

B- big goat

M- medium goat

S- small goat

B,m,s

B,s,m

M,s,b

M,b,s

S,b,m

S,m,b

Well this is interesting Katie. I think Mr Ellis has sneaked his Goat problem on here!

I really like how you’ve been systematic in giving your answers! Mrs M

B,S,M

B,M,S

M,B,S

M,S,B

S,M,B

S,B,M

Thats all the ways you can do it for 3 goats.

Well done Max. When there are 4 goats, how many more answers will there be do you think? Mr E

1234 2134 3124 4123

1243 2143 3142 4132

1324 2341 3214 4231

1342 2314 3241 4213

1432 2413 3412 4321

1423 2431 3421 4312

🙂 These are the possibilities with four goats.

Why are there so many more than 6 answers this time? How many answers do you predict there will be with 5 goats? Mrs Bowler and I have been trying to look for a pattern in the number of answers if the number of goats increases by 1. Mr E

Ok, I will give it a go and post it in the box instead .

I can see a sort of grouping method going on here? How did you arrive at this method and did you do it straight away! Post your explanation in the box Chloe! ( and tell year 5/6 we want to see more of them on here! Seriously letting the side down so far) Mrs M

bms 123

bsm 132

smb 321

sbm 312

mbs 213

msb 231

B’s’m

B’M’S

S’B’M

S’M’B

M’S’B

M’B’S

Well done Harry and Ben.

Would you use a similar system to find the answers for 4 goats?

Mr E

I’d like to see their thinking posted in the box Mr Ellis for four goats! You could introduce GM – Grandmother Goat!

S,m,b

S,b,m

B,m,s

B,s,m

M,s,b

M,b,s

abcd

acbd

adcb

bcda

badc

bdac

cbad

cadb

cbad

dacb

dcba

dacb

You seem to have a method there Harry! Could you explain what you were thinking about? Mrs M

S,m,b

S,b,m

B,m,s

B,s,m

M,s,b

M,b,s

I think I have seen a few patterns. I can predict the number of ways for 5 and 6 goats. Has anyone else noticed anything about the numbers?

Hope you’ve included your prediction on your slip in the box! Mrs M

It goes small,medim and then big but the big goat dot get a coss the bridge.

smb

bsm

bms

sbm

mbs

msb

they are all the ways you can do how many is there?

I think you’ve got a great method here. Can you try four goats now?

so m,b,s,l

s,m,b,l

b,l,m,s

l,m,b,s

Kelsey this is a great try – I’m really impressed in how you’re thinking! Look again and make sure you have all the possibilities!