Short & Sweet Math Challenge #11: Who's Next ? Message #1 Posted by Valentin Albillo on 13 Oct 2005, 7:50 a.m.
Hi all,
After several months' leave of absence, here you are, a new S&SMC challenge to
brighten up your HP programming spirit. After challenges #1, #2, ...,
#9, and #10, "who's next" ? #11, you say ? And how on earth did you came to
that bold conclusion ?
Well, that's exactly the purpose of this S&SMC#11, to substantiate that
very conclusion of yours with hard facts ... well, more like 'soft'(ware) facts, actually. Enter
The challenge
Try and write a program for any HP model that will accept a sequence of numbers, then produce
its prediction for the next element of the sequence.
For instance:
 Given the sequence 1,2,3,4,5,6,7,8,9,10, your program should
produce the value 11.
 Given the sequence 11,13,15,17,19, your program should
produce the value 21.
 Given the sequence 9,16,25,36, your program should
produce the value 49.
Your program must accept any number of elements (at least 2), then produce
the simplest reasonable prediction for the next element. No provisions
should be taken to predict further elements, just the next one.
Of course, mathematically speaking there's always a choice in selecting the
next element of an arbitrary sequence, as an infinite number of sequences are possible initially having the very same elements. Thus, for instance, the sequence:
0, 1
might continue like this:
0, 1 > 2, 3, 4, 5, ...
or like this:
0, 1 > 0, 1, 0, 1, ...
among infinite other possibilities. In this particular example, choosing
2 for the next element is simplest because in the given sequence, going
from 0 to 1 entails a (+1) increment and lacking any more information it
seems simpler to stay with it than unexpectedly reverse it to (1) for
no apparent reason. So, given the sequence above (0,1), your program is
expected to predict 2 as the next element, not 0 or any other value.
Put your program to the test
Use your program to produce the next element for the following 11 test cases:
 : 11, 13, 15, 17, 19, ?
 : 9, 16, 25, 36, ?
 : 8, 27, 64, 125, 216, ?
 : 0, 0.01, 0.32, 2.43, 10.24, 31.25, ?
 : 2, 3, 4, 1, 6, ?
 : (in radians) sin(0), sin(0.1), sin(0.2), sin(0.3), sin(0.4), ?
 : Ln(1), Ln(1.1), Ln(1.2), Ln(1.3), Ln(1.4), ?
 : Pieces of pancake (i.e: flat, 2D) obtained by N cuts: 1, 2, 4, 7, 11, ?
 : Maximum number of electrons in layer N: 0, 2, 8, 18, 32, 50, ?
 : Maximum number of pieces of (3D) cake we get with N cuts: 1, 2, 4, 8, 16, ?
 : 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, ?
Deadline
Midway next week I'll post my solution (plus comments) for the HP71B (which is
a simple, 3line program) and I'll also provide an HP15C version. You might want to try your hand at it this next weekend.
Caveat computat:
Absolutely refrain from using a PC, laptop, or PDA (unless running some HP calc emulator/simulator) to solve the challenge. A Mathematica, Visual Basic, C++, or Java solution is useless to the intended purposes of this challenge, in fact actually defeats them, and submitting one is to be considered unpolite behavior.
And who knows, you might find using your program a useful training for some outdated 'intelligence tests' ... :)
Best regards from V.
Edited: 13 Oct 2005, 8:27 a.m.
