IBM Research | Ponder This | June 2016 challenges

# Ponder This

## June 2016

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Ponder This Challenge:

This month's challenge is from Bert Dobbelaere. (Thanks!)
The marketing boys behind a large beverage brand decide to take advantage of a much-hyped soccer tournament by changing the shape of their plastic canisters. The new canisters are shaped as a truncated icosahedrons (achieved by taking an icosahedron and cutting off one-third of each edge on both ends; see http://mathworld.wolfram.com/TruncatedIcosahedron.html), which are often associated with the sport. The canisters have a small tap just above the bottom face. A pentagon was chosen as bottom, as this accentuates the symmetry of the shape. There were some concerns about the stability of the canister, which is typically placed near the edge of a table top.

On the assumption that the empty weight of the canister is negligible and its walls are infinitely thin, what is the maximum tilt angle of the table, so that the canister will never lose its balance, independent of the direction of the tilt and the filling level of the canister? If the maximum tilt angle is marginally exceeded and the canister starts to tumble, what fraction of its volume is filled with fluid?

We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com

Challenge: 30/05/2016 @ 12:00 PM EST
Solution: 01/07/2016 @ 12:00 PM EST
List Updated: 14/06/2016 @ 12:00 PM EST

Shirish Chinchalkar (05/06/2016 IDT)
John Snyder (06/06/2016 05:32 PM IDT)
Rashid Naimi (09/06/2016 02:43 AM IDT)
Graham Hemsley (10/06/2016 04:00 PM IDT)
Hugo Pfoertner (13/06/2016 10:07 AM IDT)
Siddharth Joshi (14/06/2016 04:52 PM IDT)
Mathias Schenker (14/06/2016 07:27 PM IDT)
Jesse Rearick (20/06/2016 06:22 AM IDT)
Jimmy Waters (20/06/2016 06:53 PM IDT)
Tim Lewis (21/06/2016 04:20 PM IDT)
Sergey Koposov (28/06/2016 04:57 AM IDT)
David Greer (29/06/2016 04:15 AM IDT)
Motty Porat (30/06/2016 02:45 PM IDT)
Erik Wünstel (30/06/2016 07:06 PM IDT)