Source: https://b-ok.org/book/510380/8b6eb3
Timestamp: 2019-04-24 10:47:43+00:00

Document:
Copyright © 1968 by DOVER PUBLICATIONS, INC.
Company, Ltd., 10 Orange Street, London WC2.
Tijdverdrijf Door Pu;;;;le en Spel, as published by W. J.
Thieme & Cie, Zutphen, in 1943.
simpler form; we may invert it, for example, and solve it backwards.
by the name of ticktacktoe) .
have been treated as simply as possible, avoiding algebraic formulae.
important role in the preeminently interesting theory of probability.
toward dispelling the idea that mechanics has to be a dry subject.
original a way as possible.
the counting-out puzzle 1-2-3 (§§301 and 304).
Publisher, who has taken pains to provide an attractive format.
12. More about the classification system.
Example of reversing a puzzle .
Breaking a puzzle up into smaller puzzles .
Trebles puzzle with larger numbers .
30. Extended symmetric domino puzzle .
Puzzle with dominos in a rectangle .
Salient and re-entrant angles .
Puzzle with the smallest number of angles.
Puzzle with the largest number of angles .
40. Rules of the game .
41. Supplement to the game .
42. Consequences of the rules.
43. Value of a square .
50. Remarks on the double threat.
58. Equitable nature of the game .
64. Results of John's first move I .
69. Results ofJohn's first move 2 .
70. First modification of the game .
Computing in a digital system.
Changing to another number system.
Comparison of the various digital systems.
Grouping objects according to a number system.
Relation to the ternary system.
Match game with an arbitrary number of piles .
Number of divisions into piles.
More about maxima and minima in a s('quence of numbers.
168. Even and odd positions .
II. Game of Dwarfs or "Catch the Giant!"
170. Rules of the game .
173. Correct way of playing .
176. Remarks on diagrams D, E, and G .
181. Rules of the game .
187. Rules of the game .
Proof of the assertions of §196 .
Proof of corresponding results .
Another decanting puzzle with three jugs .
Remarks on the puzzles of §§206 and 207 .
Another puzzle with four jugs .
Subtraction games in general .
217. Rules of the game .
235. Multiplication puzzle with 20 digits .
Variants of the puzzle of §238 .
Solution of the puzzle of §242 .
Solution of the puzzle of §244 .
Multiples of 7 puzzle with the largest sum.
Multiplication puzzle" Est modus in rebus"
Which are the invisible spot numbers?
Case of an odd network .
Broken line through nine dots .
295. Puzzle with twelve sums.
304. Solution of the puzzle of §30 1 by reversal .
308. Accuracy of Stirling's formula .
Which points of a traveling train move backwards?
Which way does the bicycle go?
To what systems does the principle of inertia apply?
Problem of the falling elevator.
Will the body topple over onto the smooth inclin('d plane?
How do I get off a smooth table?
puzzles, not only in their difficulty, but also in their essential nature.
which we shall call literary puzzles and pure puzzles.
luck to guess a phrase from a few fragments, or something of the sort.
though it cannot be numerically estimated).
obligation to have a more or less suitable solution available.
is done automatically by anyone who regularly solves such puzzles.
So we shall not occupy ourselves with these puzzles any further.
any language, without the nature of the puzzle changing in any way.
wrong solution to be correct.
necessarily implying a lack of intelligence.
of the cubes) can be obtained. We call these operations "moves."
questions occur that have more or less the character of a puzzle.
fruitful application of mathematics (in particular, of arithmetic).
a striking example of this.
that it is too difficult), it has to be left out of consideration.
such a way that the number of moves becomes as large as possible.
one can easily mistake an incorrect answer for a correct one (cf. §2).
moves to be the shortest possible one.
moves) is nothing else but a puzzle.
exactly how an advantageous position can be turned into victory.
puzzle quickly, but often he will not.
only with those to which the name "puzzle game" applies.
required to find some solution, then luck can indeed play its part.
positions, connected to each other again) is now presented as a puzzle.
no proper idea behind the puzzle.
clear that this form of puzzle solving will not guaran tee success.
puzzle by reasoning, if one happens to hit upon an efficient procedure.
for finding the right path, or a feeling for the right method.
solutions and there can be no others."
one goes round in a circle without noticing it.
simplicity of the method employed.
various assumptions, each of which represents a group of possibilities.
consists of this repetitive consideration of assumptions.
puzzle tree, or, more briefly, of a tree.
number terminates without requiring a subsequent digit.
been made only to save space.
because the classification is made according to a different criteriondiminishes the time required for solving by a factor of 1000 or more.
having found a digit to be inserted in some place, in a digit puzzle.
after a great deal of reasoning.
approaching this state of affairs as much as you can.
suspect that you have chosen an unsuitable division into cases.
results could not have been obtained by a single train of reasoning.
division into major cases, you should look for a better classification.
feeling the need of them when solving the puzzle.
been posed on a purely arbitrary basis.
which, perhaps, a further division into cases follows, and so on.
character of a mathematical problem.
vertices but one of the star in Figure 1 (shown with red uced dimensions).
only for the discussion that now follows.
five of the seven coins in this way.
note it down and learn it by heart.
puzzle solving of the worst kind.
connected by a line, like 3 and 6.
the puzzle with the star-shaped figure is no different.
there will be many who still cannot do it.
cannot be much greater than 1 in 100 (ef. the end of§135).
a number of times, you may show the solution in a more amusing way.
move is forbidden, then you replace it by 4.
of repeating yourself too soon.
occupies the odd-numbered vertices or the even-numbered vertices.
The chance that Peter will do this by accident is not great, of course.
order and in the reverse direction.
changed, any more than that of the quarters.
one shown at the left.
the correct preparation for another move.
into two or more smaller puzzles, which are then successively solved.
It is the principle of" divide and conquer," widely applied in mathematics, too, to reach one's goal.
difficulties of different kinds have been distributed to separate puzzles.
however, the division rather gives the impression of a simplification.
splitting up a puzzle. In Chapter II we shall give some more complicated examples.
is to achieve this in the smallest possible number of moves.
in one large square, with five white and five black pieces.
white pieces go straight across and the black pieces cross obliquely.
black pieces straight, but this comes to the same thing.
true that 2 has been located to the right of d, but since 2 is not connected directly to d, this is of no importance.
crossing is possible in 8 moves (and not less).
The first column gives the possible orders of moves 1,2,3,4, b, c.
for the puzzle of the even pieces only). The same number of possibilities applies in the case of the puzzle with the odd pieces.
pieces). Obviously there the crossing can occur in 2 x 8 = 16 moves.
use 1, 2, 3, 4 for the white pieces, and a, b, c, d for the black pieces.
Ic3a4b2d, cld3a4b2, cla3d4b2, c3ald4b2, c3a4bld2.
15-3, 11-17,3-11, 1-19,5-13, 19-15, 13-1, 17-5.
for the original puzzle, using white and black pieces alternately.
next moves back, with A, until it is between P and Q.
is always to the right of L.
that in Figure 11 cars A and D be interchanged, and also Band C.
left past P, or to the right past Q.
order of the cars and the engine can be achieved.
turntable and pulls A and B together to the left.
initial digit 0) that are written with the same digits as their treble.
placed to the right of the number.
this way if we had required all 6- or 7-digit numbers, say.
say that the desired numbers have a digit sum that is divisible by 9.
digit 1, 2, or 3 in its treble, and so on.
are composed of the same digits as their trebles.
digit is the last in the number or is followed by 0, 1, or 2.
0, 1,2 and the ordinary 3 (which, by the way, turns out not to occur).
italicized 3, the bold 3, the 4, the 5, the ordinary 6, and the italicized 6.
with an ordinary digit at the right.
2(h - b) + (m - i) = 2s - 9(2h + m).
= (i - m) + 2(0 - I).
the word dead (in roman type).
For the remaining 10 combinations all equations are satisfied.
is to permute the digits in question.
number of bold digits = number of high digits, etc.
numbers it is not necessary to know this.
we admit 0 as initial digit.
§24 do not hold. Thus, only the sequences 857142 and 973026 remain.
(72-86--4-9) 248976, 249876; (72-4-5-9-9) 249975.
which are written with the same digits as their treble.
86374, 98624; 625013, 875124, 986374; 8750124, 9875124.
occur, and as many ordinary digits as even digits, in every sequence.
a bold digit would always have to be followed by a bold digit again.
875124-0 and 875124-9 drop out.
not yield a further decrease of the number of possibilities.
can be done in six ways; in all this gives 2 x 6 = 12 solutions.
is bold). It is immaterial whether 05 is placed before or after 287.

References: §196
 §238
 §242
 §244
 §30
 §2

§24