9 I 6
© Laurent Dubois 2001
PART 2 (visuo-spatio-algorithmic) SCORING
SCALE PROJECTED
NORMS
D.
1) What time is it ?
2) Which is the odd one
out?
a b c d e
3) Which two of the following figures do not belong to the same family as the three others?
a b c d e
4) analogy
: 
:: 
: ?
5) The square of squares
Here is a square constituted by 4 small squares.
Having known that figures 1 , 2 , 3 or 4 should be distributed at random each
in one of four small squares, and that every small square can be put in
rotation of 90 °, 180° or 270°, how many different configurations are
possible, in other words, how many big different squares as it is could obtain?
6) The "Fractal Chessboard"
You have a
normal chessboard. You keep a version of that chessboard - we call it
chessboard A; you make 32 scale models of that chessboard, named chessboards A'
so as to replace the 32 white cases of chessboard A by the 32 scale model A'.
Therefore, you have a new chessboard with 32 black cases and 32 chessboards A'. We'll name it chessboard
B. You keep a version of that chessboard B. After that, you make 32 scale
models of that chessboard, named chessboards B' so as to replace the 32 black
cases of chessboard B by the 32 scale model B'. Therefore, you have a new
chessboard with 32 chessboards B' cases and
32 chessboards A' cases. We'll name it chessboard C. You keep 2 versions of that chessboard C;
you make 64 scale models of that chessboard, named chessboards C' so as to
replace the 32 white cases of chessboard C (i.e. cases corresponding to white
cases on initial chessboard A) by 32
scale model C'; this new chessboard is named C1. You take now your second
version of chessboard C and you replace
the 32 black cases of that second chessboard C (i.e. cases corresponding to
black cases on initial chessboard A) by the last 32 scale model C'; this new
chessboard is named C2.
You compute
how many self-coloured black and white cases
each chessboard C1 and C2 contain? Then you make "number cases
chessboard C1 minus number cases chessboard C2". You have a number. We
call this number N.
The
question is: what is the square root of the number you obtain when you add the
smallest possible square number to the number N necessary to have another
square?
7) the marvellous motive
which is the correct figure to complete the
motive?
a b
c d e f
g h
8) The Hypercube’s Declination
a) Is it possible to draw a tesseract with an unique broken line? (you
cannot lift up the pencil nor retrace yours's steps) If yes, number the lines
b) How many distinct regular volumes can you clearly detect in this
Hypercube?
c) Three dices joined side by side in an Hypercube. One face is
given: face one.
The
question is: how much configurations are possible with the 6 different values?
Please, draw them.
d) Complete the last figure
e) Add the missing point in the last figure
f) Complete the last figure algo
g)
:
::
: ? 
h)
:
::
:
?
i) What is the missing number? (the smallest number, viewed with
difficulty, is 24)
j) What is the maximum number of
completely bounded volumes that can be formed by all the interpenetrating
regular volumes of an Hypercube, considering only the surfaces of the volumes
as bounds and counting only volumes that are not further subdivided? Prove your
answer.
k) The Hypercube’s Labyrinth
------------------------------
Which is the missing line?
9) The moebius Chessboard
a) Find the number of non-attacking queens necessary to cover a mobius
strip chess-board of 64 squares and prove that this number is minimal.
b) Find the maximal number of non-attacking queens necessary to cover a
mobius strip chess-board of 64 squares.
10) The Magic Puzzle
You can
solve the problem on the following page :
http://www.fitzweb.com/brainteasers/puzzlers.shtml
Don’t
forget to write your name in the appropriate field.
11) Knight’s tour
The
objective of this puzzle is to pass all the squares of the board with the
knight, making only legal moves. A legal move for the knight is shaped like an
L. Up or down two squares and over one square. The knight starts in a random position.
Click on the square that you want to reach from there. It will be occupied by a
new piece. Continue until the whole board is filled.
solve the
puzzle at the following adress and print your solution
http://enchantedmind.com/puzzles/knights/knight.htm
12) Sphere
13) Which is the
following figure?
14) Abyss
Part : Part: Part: Part:(...) :: Whole : ?
15) The Bishops’s Conversion
The goal is to move all the white bishops to the top and all the black
bishops to the bottom
Alternate
moves - white moves first, then black, then white, etc.
You can't
place a bishop on a square where it can be captured by an opposing bishop
You may only
make valid chess bishop moves (diagonal only and as many available squares as
one wants in the chosen direction)
You can
solve the problem on the following page :
http://www.fitzweb.com/brainteasers/index.html
Don’t forget to write your name in the
appropriate field.
ÓNEUROLAND2000Ò
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