Using your Head is Permitted

March 2017 riddle

UPDATE (3 March): In the definition of the problem I said you need to word the function in a way that makes it easy to compute with "a pocket calculator". I did not specify which pocket calculator, but I did include a link to a specific one. Several readers sent in solutions that would work on some pocket calculators, but not on this specific one, because they use constants or functions that this calculator does not have. As I did not specify in advance that I mean this specific pocket calculator, I will give credit to solutions that work on other typical pocket calculators of a similar type. However, solutions that work on my specific choice of pocket calculator will be denoted by an asterisk.

Dear readers,

This month marks the 10 year anniversary for Using your Head is Permitted. To be honest, I never thought we'd make it this far. And we wouldn't have -- if it wasn't for your constant support and encouragement, and for the riddles you keep sending in.

Thank you all, from the bottom of my heart. Keep riddling. Keep solving. Keep enjoying maths. Maths -- despite what many school-teachers teach and many school-children learn -- is there to be enjoyed; it is its one purpose.

Paraphrasing Paul Lockhart, maths may have some mundane practical uses, but making these the focus of our teaching and learning of the subject is like teaching third-graders to read by having them fill out purchase orders and tax forms. When asked what one should do with young children in math class, Lockhart answers:

"Play games! Teach them Chess and Go, Hex and Backgammon, Sprouts and Nim, whatever. Make up a game. Do puzzles. Expose them to situations where deductive reasoning is necessary. Don't worry about notation and technique, help them become active and creative mathematical thinkers."

This advice, given for the teaching of third graders, I believe to be sound in every maths level. Yes, notation is important, but it's important only because it helps us communicate maths. More important is that we have things that we want to communicate, or things that we are open to listen to. Indeed, so many times new readers begin their first e-mail to me with "I apologise if I am not using the right notation." These readers tend to find their names very quickly on the solver list. I have never yet disqualified a solution that I understood and recognised to be mathematically sound, no matter how it was worded.

Two years ago, at Using your Head is Permitted's 100-riddles celebration, I ran through a listing of the site's many accomplishments over the years: the quantity and diversity of solvers, the riddles whose quality is high enough to find themselves time and again in top-tier journals. I won't reiterate the same list now. I will mention, however, that increasingly the site gets written about, such as in this article in Vinculum (publication of the Mathematical Association of Victoria) dedicated entirely to the site.

But enough about us. Last month I announced a competition for the anniversary riddle, and the winning riddle is one sent to me by Ori Pomerantz. Many thanks, Ori! Congratulations!

This is not the first time Ori has contributed a riddle, but I haven't seen him on the site since 2009 (!!), making him one of what appears to be the large majority of this site's readers, being the readers who enjoy the reading, but do not send in solutions. Glad to see you (and you all) still with us.

Ori's riddle is the following:

Find a function, f:ℝ→ℝ, such that f can be differentiated infinitely many times, such that its 10th derivative equals exactly f itself, and such that no derivative between the first and the 10th (not inclusive of the 10th) equals f.

Please send your answer in a format that would make values of the function easy to compute with a pocket calculator.

List of solvers:

Uoti Urpala (*) (2 March 05:03)
Itsik Horovitz (*) (2 March 09:05)
JJ Rabeyrin (*) (2 March 10:46)
Lin Jin (*) (2 March 13:31)
Yuping Luo (*) (3 March 01:58)
Teng Li (*) (3 March 03:31)
Mithil Ramteke (3 March 04:41)
Zhangyi Hu (*) (3 March 11:28)
Dan Dima (*) (4 March 01:25)
Hamidreza Bidar (4 March 05:28)
Alexander Ruff (*) (6 March 07:29)
Andreas Stiller (*) (6 March 10:24)
Lorenz Reichel (*) (7 March 07:13)
Jim Boyce (*) (7 March 10:04)
Omer Angel (*) (7 March 12:31)
Tianzong Zhang (*) (9 March 00:18)
Oded Margalit (*) (9 March 10:32)
Harald Bögeholz (9 March 12:28)
Liu Yi (*) (12 March 14:55)
Philipp Reinhard (*) (15 March 09:25)
Serge Gautier (*) (16 March 04:06)
Jens Voss (*) (17 March 16:51)
Xiao Liu (20 March 15:19)
Adrian Neacsu (*) (23 March 08:51)
Oscar Volpatti (*) (29 March 23:47)

Elegant and original solutions can be submitted to the puzzlemaster at 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.


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