## The Big Totem Pole Puzzle: Four Squares

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The Totem Pole shape consists of Orange, Red, and Blue blocks. **Which volume is the smallest**: the total volume of the Orange blocks, the total volume of the Red blocks, or the total volume of the Blue blocks?

Peter Grabarchuk created this especially for Smartkit : )

also- Carl H, while doing an interesting analsyis of **Untouchable 11**, has created a variant challenge that should be a litter easier than the ‘impossibly hard’ level. Scroll down to comment 19 here.

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BillyPilgrim| Profile January 21st, 2009 - 11:45 pmThe orange blocks, since there are none of them.

RK| Founder | Profile January 22nd, 2009 - 12:06 amok Pilgrim, maybe I do need an eye exam-

yellow blocks it is

almost forgot! -will keep any submitted answers masked until around Monday

sprice22| Profile January 22nd, 2009 - 12:13 ammy guess is they will all be the same but im gonna try to work it out.

sebbie3000| Profile January 22nd, 2009 - 11:40 amAt a complete brief glance over – I’d go with the red blocks. But I only looked at the picture for about 5 seconds and went with my gut instinct.

michaelc| Profile January 22nd, 2009 - 4:56 pmSince the widths are all the same, the problem can be reduced to which color has the least surface area which isn’t much help.

It looks like they are all just about even, and I won’t even try to calculate all the odd shapes in the stack mathematically!

So my guess is they are all equivalent.

bizarette18| PUZZLE MASTER | Profile January 22nd, 2009 - 6:18 pmI think red has the least. When you combine the quarter circles with the edgy bits you get 4 and 3/4 big squares for blue and yellow; but you’re missing one quarter edgy bit for the red, if I counted correctly.

bilbao| Profile January 23rd, 2009 - 1:54 amRED are the smallest

Proportions: Blue-19 : Yellow-19 : Red-18.785

Shawn| PUZZLE GRANDMASTER | Profile January 23rd, 2009 - 9:51 amI’m going with red, although blue is tempting…

fuzzy| Profile January 23rd, 2009 - 1:33 pmRed blocks have the smallest volume.

I ignored the 3D aspect of the puzzle since the 3rd dimention is always the same, and went ahead to calculate the areas of each color in 2D.

Let’s assume the side of each square is 2, thus the radius of the inscribed circle is 1. The area of an entire square is 4, and the area of a full cirle is pi.

Without going too much into the boring math, I will just say that each color blocks have the following areas of the facing sides:

Blue: 23-pi or approximately 19.86

Red: 22-pi or approximately 18.86

Yellow: 19

Thus, red sides have the smallest area and red blocks have the smallest volume.

Ari| Profile January 25th, 2009 - 4:21 amThe red volume is ~1.13% smaller compared to the orange(yellow) and blue volumes, which are equal.

I was too lazy to figure it out on a piece of paper, so I just replicated the blocks in a cad program and went from there :/

Puzzlinks Roundup (weekly) » puzzlinks.com| Guest January 25th, 2009 - 8:31 am[…] The Big Totem Pole Puzzle: Four Squares | Smartkit Puzzles and Brain Teasers […]

Someone| Profile January 25th, 2009 - 2:14 pmRed is the smallest, with 18 + pi/4

Yellow and Blue are the same, with 19 each

RK| Founder | Profile January 26th, 2009 - 11:03 amSomeone, Ari, Fuzzy, Shawn, Bilbao, Bizarette18, Sebbie3000 are correct:

check the solution here: http://smart-kit.com/wp-conten.....lution.jpg