Help! Stumped on maths question!

[Hollyhead]

DC has been working on this for 15 mins, we’ve tried trial and error but we’re both running out of steam!

I think each long side is 3 x 1.7 + 1 x 0.9 and each short side is 2x 0.9 + 2.2.

So

6x0.9
6x1.7
2x2.2

2.2 + 0.9 + 0.9 = 4m

1.7 + 1.7 + 1.7 + 0.9 = 6m

You need double this.

So 14 pieces of fence.

The 6m side is 1.7 +1.7+1.7 +0.9
The 4m side is 2.2+0.9 +0.9

Double them up and count the pieces required.

thank you! Did you all just do trial and error? I think our methods failed 😂

I would say 14 ( assuming all side are to be fenced):

Short side = 1 x 2.2 + 2 x 0.9, so 3 pieces
Long side = 1 x 0.9 + 3 x 1.7, so 4 pieces

Urgh...Sparx Maths is not popular here

Need -
2 x 2.2m
6 x 0.9m
6 x 1.7m

(2.2+0.9+0.9 = 4m, 1.7+1.7+1.7+0.9 = 6m, then double for all 4 sides)

So to get 6m you need 1.7m x 3 and a 0.9m
to get the 4m you need 2.2m and 2 x 0.9m
that needs to be times 2 for the 6m and 4m

Used logic ...
They question asks what combination uses the fewest pieces of fence.
Logic tells you to use the longest pieces you can.

So start with the longest length, and add on next longest until you find a combination that works:
For the 6m side
2.2 + 2.2m = 4.4m, need 1.6m more to get 6m, which isn't possible,
So try 2.2m + 1.7m +1.7m ... also doesn't work,
so try 1.7m +1.7m + 1.7m + 0.9m =6m
Use the same process for the shorter side.

It’s the smallest number of pieces of fence needed though . Lots of these replies are the smallest total length of fence (least waste). It’s a rubbish question.

You can't cut or bed though so all the answers so far are right unless I'm missing something

But there is no waste? That's the point of the question - you're not allowed to break lengths of wood.

So 4m is 2.2 x 2 = 2 pieces or 4 total
6m is 2.2 x3 or 2.2 x2 plus 1.7 = 3 pieces or 6 total
therefore 10 total

Neither of these add up to a round number though 😂

But to get back to 4m you'd have to cut it? Same for 6m?

I agree with the pps who say that the fence lengths need to sum to exactly 6m and 4m

6 = (1.7 x 3) plus 0.9 . 4 fence pieces.
4 = 2.2 + (0.9 x 2) . 3 fence pieces.

Total 7 pieces.

Doubled to give 14.

It says no cutting or bending, but you could presumably overlap the pieces. So I would say the answer should be 10 pieces.
I’m sure they want the answer to be 14 pieces as worked out above though!

It doesn’t say anything about ‘round’ numbers. To get the smallest number of pieces you would overlap I guess. It’s a rubbish question.

@Londoner256 , Overlapping the pieces sounds like a good idea. I agree with 10 in that case.

But what’s the point in having a path across the garden if there are no gates in the fence? Are we meant to think it’s a low fence you can step over?

I wouldn’t say overlap is allowed? If bending and cutting isn’t.

So for 4m you need a 2.2+0.9+0.9
And for 6m you need 1.7+1.7+1.7+0.9
then doubled for each side etc.

So yes, trial and error.

But you wouldn't overlap fence panels in real life would you? That's a hell of a lot of over thinking 😂😂 it's obvious that the question is about adding and subtracting decimals to get to a round number, it's not a logic puzzle!

I've got same as previous posters,14 panels altogether.
3×1.7m +1×0.9m=6m ×2
1×2.2m+2×0.9m=4m ×2

How about this as a logical way to think it out if the numbers don't immediately suggest anything to you.

You want the least number of pieces so start with the longest section
1 x 2.2 = 2.2
2 x 2.2 = 4.4
3× 2.2 = 6.6

Can you get to 4 or 6? Not exactly so try adding the next longest piece

2.2 +1.7 = 3.9 close but no 0.1s available
2.2 + 0.9 = 3.1 so keep going
2.2 + 0.9 + 0.9 = 4 bingo

Now I'm wondering if drawing a tree would help to work out what lengths are possible.

Start with 2.2 add each option in turn

(If you call the lengths a,b and c you're working out
a + a,b or c then b+ b or c then c+c gives all combinations of two pieces.
next level branches similar
a+ a + a,b or c then a+b+ b or c etc to end up with all combinations of 3 pieces.)

Rubbish formatting but first line one piece second line 2 pieces etc

......................................2.2....................................1.7..........................0.9
4.4.......................3.9................3.1 3.4.............2.6 1.8
6.6x....6.1x...5.3 5.6....4.8 4.0* 5.1....4.3 3.5 2.7
X X X X ....5.7 X...6 5.2 4.4

Which shows you can get the required lengths with paths 2.2+0.9+0.9 and 1.7+1.7+1.7+0.9 and no other combinations with less pieces so you can be confident.

I think it’s 14panels, but question is are you supposed to leave a space for a gate? Logic would tell you you need to.

Glad I don’t have to help with this sort of homework!

10 × 2.2 for the smallest amount