Igloos Gone Wild

Igloos Gone Wild

December 15, 2013

In cold, cold places, people sometimes live in igloos, small homes built of blocks of ice and snow. It’s not very warm inside an igloo, but it’s warmer than the outside if it’s the kind of place where an igloo won’t melt for weeks! Real igloos are built by stacking blocks of ice or packed snow in a spiral that goes around on top of itself, not in rows that start and end at the same height. Usually it’s plain white ice or snow cut from nature, but one couple decided to make their own multicolored igloo. They saved up box-shaped milk cartons, filled them with water and a few drops of food coloring, then let them all freeze into beautiful colored ice blocks. They packed the blocks using snow to hold them, and here you see the result, with a light inside to show off the amazing colors. If you live in a place with a cold winter, this is a project you can try, too – if you drink enough milk beforehand!

Wee ones: If the couple used blue, red, green, orange, and yellow blocks, how many colors does the igloo have?

Little kids: If the main body of the igloo uses 100 blocks and the entrance uses 40, how many blocks were used?  Bonus: If 10 of those blocks are pink, how many blocks are other colors?

Big kids: If the igloo builders saved 50 cartons of milk, and each carton holds 8 cups, how many cups of milk did they have to drink to make this igloo?  Bonus: If it took 5 ½ hours for the water to freeze through and the first carton was filled at 10:30 am, at what time was the first block ready for building?

The sky’s the limit: If the igloo has (roughly speaking) 10 layers, and each layer has 4 more blocks than the one above it, and it uses 600 blocks total, how many blocks are there in the bottom biggest layer?

 

 

 

Answers:
Wee ones: 5 colors!

Little kids: 140 blocks.  Bonus: 130 non-pink blocks.

Big kids: 400 cups of milk.  Bonus: At 4 pm.

The sky’s the limit: 78 blocks. If there are b blocks in the bottom layer, then the 10 layers have
b+(b-4)+(b-8)+…up to (b-36) blocks. This is the same as 10b – 4 x (1+2+3…+9), or 10b – (4 x 45) (if you know the triangle shortcut formula: for a triangle with the biggest number t, the total is t x (t+1)/2).
So we now have:
10b – 180 = 600
10b = 780
b = 78 = the number of blocks in the bottom row.

And many thanks to Zeland C. for suggesting this topic!

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Laura Overdeck

Laura Overdeck

Laura Bilodeau Overdeck is founder and president of Bedtime Math Foundation. Her goal is to make math as playful for kids as it was for her when she was a child. Her mom had Laura baking while still in diapers, and her dad had her using power tools at a very unsafe age, measuring lengths, widths and angles in the process. Armed with this early love of numbers, Laura went on to get a BA in astrophysics from Princeton University, and an MBA from the Wharton School of Business; she continues to star-gaze today. Laura’s other interests include her three lively children, chocolate, extreme vehicles, and Lego Mindstorms.

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