This month marks "Using your Head is Permitted"'s 75th riddle. To celebrate the
anniversary, here's something slightly unusual.
Consider the following puzzle:
You have To do so, all you have at your disposal are balance scales. You can put any subset of the coins on any side of the scales, but you cannot put on the scales anything other than the coins themselves. Naturally, you also cannot place a single coin multiple times on the scales in any given weighing (though the coins can be reused between weighings).
The question is: what is the minimum number of weighings, I will give references about this riddle on the solution page, as well as a more thorough explanation of what makes it a special (75th anniversary) riddle. For now, I will say that the success criterion for this riddle is somewhat fuzzier than in our usual riddles.
To get your name on the solvers list, state and prove the complexity of
L f(n)≤B(n)≤H f(n)
holds. Finding
A special mention (and/or an asterisk next to his/her name) will be given to
anyone who can say more interesting things about
(If I deem the observation interesting enough, a special mention and/or a
place on the solvers list can be
awarded even to someone who did not solve the basic question about the
complexity of Such extra questions that you may wish to tackle include - Give tighter upper bounds than the complexity ones.
- Give tighter lower bounds than the complexity ones.
- Determine if
*B*(*n*) is a monotone sequence.
Good luck! And thank you for reading Using your Head is Permitted and keeping it going for 75 months already! |
## List of solvers:Omer Angel (5 May 04:41)Thomas Mack (24 May 17:23) Liubing Yu (25 May 00:25) |

Elegant and original solutions can be submitted to the puzzlemaster at __riddlesbrand.scso.com__.
Names of solvers will be posted on this page. Notify if you don't want
your name to be mentioned.

The solution will be published at the end of the month.

Enjoy!