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norman182 · Boot Joined: 16 Apr 2006 Posts: 14

#127 Card Houses

**Posted:** Sun Jul 30, 2006 8:26 am

ne0x

Draw a picture!

**Posted:** Sun Jul 30, 2006 12:11 pm

DarkHuman

i get 23" or 584.2 mm. Set up the 38 cards myself.
__1
/\/\4
____3
/\/\/\ 6
_____4
/\/\/\/\8
______5
/\/\/\/\/\10

**Posted:** Sun Jul 30, 2006 7:47 pm

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Cinana

Actually, I believe that is too many cards.

I studied this while at work today, and came up with this layout.

**Posted:** Sun Jul 30, 2006 11:45 pm

Cinana

hmm...maybe i did that wrong.
I don't have the patience to try to make these cards stand still while I try to stack them, but after some measuring, you can not stand the cards long side standing, and expect to get a base card to stay on top.

So, after much frustration at my husband (he's telling me that I have it right, but after physically showing him, he's shut up)

you must lay the cards long side on their sides for the 30 degree angle to work.

the answer then becomes

**Posted:** Mon Jul 31, 2006 12:18 am

KingOfWrong · Boot Joined: 05 May 2006 Posts: 45

Remember, the cards meet at 30 degrees, which means they're at 15 degrees to the vertical - trigonometry only works on right-angled triangles, after all.

**Posted:** Mon Jul 31, 2006 1:57 am

ne0x

Redrew my picture...

It looks like Cinana's now, and I get:

**Posted:** Mon Jul 31, 2006 8:11 am

thereverendeg

Confirmed Solve

**Posted:** Mon Jul 31, 2006 2:19 pm

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Cinana

I asked my friend who is the math whiz to check my work, and I was certainly wrong...However, I was not that far off. Misunderstood mostly.
LOL Very Happy

After doing the math the correct way, the final answer is what thereverendeg said, if you round up. To 3 decimal places the answer would have also been 71.479.

So, don't mind me...I am just mathematically challenged.

**Posted:** Mon Jul 31, 2006 11:18 pm

xandert_86 · Boot Joined: 14 Apr 2006 Posts: 16 Location: Where I Be

Okay, it may have been a while since I've done proper maths, but I thought my basic trig was okay - S ^o _h C ^a _h T ^o _a

**Posted:** Wed Aug 02, 2006 12:05 pm

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ne0x

**Posted:** Wed Aug 02, 2006 1:16 pm

Cinana

My diagram that I wrote up top is the correct diagram. I noticed you only put "4 tiers". Ne0X said it right. Have a look at the roofs.

You are very very close to the correct answer. Just missing one aspect. Then after you have come up with the answer (yours may come with figure with 3 decimal places, just round up.

Good luck.

**Posted:** Thu Aug 03, 2006 1:20 pm

mDuo13

So I took photos. The tallest one I could make with 38 cards was a little short of the theoretical maximum - apparently I overlapped a little much on the horizontal cards, and the angles of some pairs were too wide - but it was good times overall. Thanks to whoever had the accepted answer. I love doing this stuff, but I hate having to fuss over their specific answers, and I wasn't about to start doing all the math (though I could... I just didn't want to).

Anyway, enjoy. The first pic is the tower with 38 cards. The second is 40 cards, but the proper number of levels. Sorry about the blur; my camera's batteries died midway through taking the pictures. (That's also why I didn't have room to clean the mess out of the picture.)

**Posted:** Thu Aug 03, 2006 2:50 pm

ne0x

That rocks!

There ought to be a gallery for pictures of solutions to cards. There are more than one that involves baking, building or making something.

**Posted:** Thu Aug 03, 2006 5:57 pm

bobonacus · Greenhorn Joined: 22 Apr 2006 Posts: 4 Location: berkshire

great puzzle ... and a great card stack Cool

years since i've used soh cah toa

see http://www.mathsrevision.net/gcse/pages.php?page=39

**Posted:** Thu Aug 03, 2006 8:30 pm