DeanUK2US

I'll leave it for the other guys who claimed it was right to explain.

I've got it... but will post in a minute...

DeanUK2US

Okay, how is this 32?

N1cky

You would think the teacher would have explained to them rather than just telling them the answer

I won't claim to have worked it out, I had to google it and i'm still slightly confused

A word triangle is created by taking a word, putting the first letter on the first line, putting two of the second letter on the next line, three of the third letter on the third line, et cetera. Given the word TEASER, the word triangle would look like this:

T
EE
AAA
SSSS
EEEEE
RRRRRR

If you begin at the top and start spelling TEASER by either moving to the letter directly below the letter you are currently on or by moving to the letter that is immediately to the right of the letter below the letter you are currently on, you could use several different paths to spell the word. For instance, if your path takes you to the third 'A' you could either go to the third 'S' or the fourth 'S', but not to the first or second 'S'.

Answer
2^5 = 32

SirSteveUK

Strongl;y suspect that its not a simple answer - rather a matter of drawing paths from each letter you choose to the next and so on - you can only go to the next letter if it is directly below - or one to the left or one to the right - so if you chose the leftmost H - you have two O's to choose from - but if you choose the rightmost H - then you have all 3 O's to choose from

I don't know if this is the answer - but it would limit the choices and possibly end up like a Fibonacci sequence=

2 + 7 + 10 + 13 = 32

Ozzidoc

We (you guys) didn't.

I suspect that the teacher was applying either some other kind of randomly made up rule, or simply miscalculated

ChocolateBabz

He apparently gets 80% for getting it wrong anyway as he showed his working out and explained his process and remembered to have it signed by yours truly. It's not the 105% he usually gets but hey I'll take the 80

snowbunny

Yeah, but the teacher did not give the path restriction. The example you give looks like paths to leaf nodes on binary trees, whereas the original (with no description) is a factorial. Tell the teacher to read Knuth's work on computer algorithms before assigning homework!

Ozzidoc

That's what I meant

DeanUK2US

I can see why the original answer of 6! was wrong because we were not specifically spelling 'ghosts', we were just giving every possible combination of letters, so we were including gibberish like 'hostsg', 'ostshg', etc.

N1cky

Can't wait for my kid to reach 5th grade

ChocolateBabz

Thanks snowbunny - I didn't understand the big words but you are correct in that we did not get any path restriction - 3 other kids got the answer 720 and about half the class got it wrong - and then the teacher told them that next weeks problem would be a hard one . Maybe we could make this a weekly challenge

snowbunny

I tell ya, my 4th grader brought home a logic puzzle - the kind found in game magazines to fill in - and it was hard! It was three way instead of simply two way - a person's name, what they saw, and how they felt about seeing it!

They used "boy" and "girl" as some of the clues, but the names they gave these kids weren't like John, Bob, Mary and Anne. They were modern and inclusive like Brittany - that was one of the names. I kept muttering "Brittany had better be an effing girl" under my breath.

Duncan Roberts

Actually no, as written the 6! is correct (and would only spell ghosts) as was pointed out. It's only when you add the route restriction you get a reduced number of computations. For instance in 6! (and as written in the OP) the sequence 1, 2, 1, 4, 2, 1 would be acceptable and spell GHOSTS but with the made up restriction that you can't go backwards when you move down a line it is not acceptable. I would write to the teacher and say they are wrong if they really did word the question like that.

dbj1000

Apparently your 10 seconds of thought didn't give you time to understand your own answer then. 6! is the correct answer to spell GHOSTS (and only GHOSTS) if there is not path restriction moving from one row to the next.

dbj1000

Given that my kids are doing the Fibonacci sequence in 5th grade right now, I'm pretty sure you're right. There must have been a rule restricting selection of the letter in the next line, but to arrive at 32 I'm buggered if I can work out what that rule was. It doesn't seem to be the one you describe, since I arrive at 40 that way.

Whether that rule was explained by the teacher is in some doubt, since factorials and the Fibonacci sequence are way over the heads of many teachers who are supposed to teach the subject.