Mathematical_Recreations-Kraitchik-2e

Recommendations

Info

The Calendar111MONTHMJanua~ ........ 0Februa~ ....... 3March ......... 3April .......... 6May ........... 1June ........... 4July ........... 6August ......... 2September ...... 5October ........ 0November ...... 3l)ecember ...... 5FIRST Two DIGITSOF THE YEARCGregorian Calendar15, 19,23, 116,20,24, 017, 21, 25, 518,22,26, 3Julian Calendar00, 07, 14, . . . 501, 08, 15,· . . 402, 09, 16, . 303, 10, 17, . 204, 11, 18, . 105, 12, 19, . ()06, 13, 20, . 6LAST Two DIGITS OF THE YEAR I Y00 06 17 23 28 34 45 001 07 12 18 29 35 40 46 102 13 19 24 30 41 47 203 08 14 25 31 36 42 309 15 20 26 37 43 48 404 10 21 27 32 38 49 505 11 16 22 33 39 44 50 1 651 56 62 73 79 84 90 057 63 68 74 85 91 96 152 58 69 75 80 86 97 253 59 64 70 81 87 92 98 354 65 71 76 82 93 99 455 60 66 77 83 88 94 561 67 72 78 89 95 6
112 Mathematical RecreationsDATE YEAR DAYMONTHCENTURYGREGORIAN JULIAN- 22,50,78 Th.W --- 27,55,83 T-- 13M --- 26,54,82 SSat.--6,13,20,27- - 25,53,81 F April - - July 21-- 7Th. --- 24,52,80 WT --- 18,46,74 M-- 8S --- 23,51,79 - - Sat.F --5,1~,19,26- - 16,44,72 Th. Sept. - - Dec. --9W- 21,49,77TM- 20,48,76S-- 10Sat.--- 14,42,70,98 FTh. --4,11,18,25- - 19,47,75 W Feb. -- June 15,23-- 11T --- 12,40,68,96 MS --- 17,45,73 -- Sat.20 -- 12F --- 11,39,67,95 Th.W --3,10,17,24,31- - 10,38,66,94 T March - - Nov. -- 6,13M --- 15,43,71,99 SSat.--- 8,36,64,92 F17 -- 14Th. --- 13,41,69,97 WT --2,9,16,23,30-- - 7,35,63,91 - M -- Aug. -- 1,15S --- 6,34,62,90 - - Sat.F --- 5,33,61,89 Th.18,22 - - 2,16w--- 4,32,60,88 TM --1,8,15,22,29- - 9,37,65,93 S Jan. -- May -- 3,17Sat.--- 3,31,59,87 FTh. --- 2,30,58,86 W19 -- 4,18T --- 1,29,57,85 MS --7,14,21,28- - 0,28,56,84 - - Sat. --Oct. 16 -- 5.19FIGURE 17. Perpetual Calendar.
Page 2 and 3:
MathematicalRecreationsMAURICE KRAI
Page 4:
TOMR. DANNIE HEINEMANwho encouraged
Page 7 and 8:
8 Mathematical RecreationsMr. W. W.
Page 9 and 10:
10 ContentsPAGECHAPTER SEVEN.1. Def
Page 12 and 13:
CHAPTER ONEMATHEMATICS WITHOUT NUMB
Page 14 and 15:
M athematics Without Numbers 15he r
Page 16 and 17:
Mathematic8 without Numbers 17word
Page 18 and 19:
Mathematics witlwut Numbers 19way a
Page 20 and 21:
Mathematics without Numbers 21~ I(h
Page 22 and 23:
Ancient and Curious Problemsto the
Page 24 and 25:
Ancient and Curious Problems 25Any
Page 26 and 27:
Ancient and Curious ProblemsSolutio
Page 28 and 29:
Ancient and Curious Problems 29Semp
Page 30 and 31:
A ncient and Curious Problems 31Ans
Page 32 and 33:
Ancient and Curious Problems 33monk
Page 34 and 35:
SolutionNo.Ancient and Curious Prob
Page 36 and 37:
Ancient and Curiou8 Problemab+da+ci
Page 38 and 39:
Ancient and Curious Problems 89and
Page 40 and 41:
Ancient and Curious Problems 41t =
Page 42 and 43:
thenA ncient and Curious Problemsx-
Page 44 and 45:
Numerical Pastimes 45desired number
Page 46 and 47:
Numerical Pastimes 47Mr. Thebault g
Page 48 and 49:
Numerical Pastimes 49threes I find
Page 50 and 51:
Numerical Pastimes(3) 16ab + c = 16
Page 52 and 53:
Numerical Pastimes 53If the standar
Page 54 and 55:
Numerical Pastimes 55consists of k
Page 56 and 57:
Numerical Pastimes 57sponding to th
Page 58 and 59:
Numerical Pastimes 592. Think of a
Page 60 and 61: Numerical Pastimes 61the result. Or
Page 62 and 63: Numerical Pastimes 68If we subtract
Page 64 and 65: ABCDEFGHIJKLM IIN 0 P Q R STU V W x
Page 66 and 67: Numerical Pastimes 67progressions.
Page 68 and 69: Numerical Pastimes 691 (n + d - 2)!
Page 70 and 71: Numerical Pastimes 71Two or more pr
Page 72 and 73: Numerical Pastimes 73= 8. m2(m + 1)
Page 74 and 75: Numerical Pastimes 75Thus, in order
Page 76 and 77: Numerical Pastimes 778. AUTOMORPHIC
Page 78 and 79: Numerical Pastimes 79primality has
Page 80 and 81: Numerical Pastimes 81products with
Page 82 and 83: Numerical Pastimes 838. QUI)TRO UVE
Page 84 and 85: Numerical Pastimes 85There are many
Page 86 and 87: Numerical Pastimes 87if a player A
Page 88 and 89: Numerical Pastimes 893. CHINESE RIN
Page 90 and 91: Numerical Pastimes 91rings. If the
Page 92 and 93: Numerical Pastimes 93others getting
Page 94 and 95: CHAPTER FOURARITHMETICO-GEOMETRICAL
Page 96 and 97: SinceArithmetico-Geometrical Questi
Page 98 and 99: A rithmetico-Geometrical Questions
Page 100 and 101: Arithmetico-Geometrical Questions 1
Page 108 and 109: CHAPTER FIVETHE CALENDARTIME can be
Page 112 and 113: The Calendar 113scale). For the mon
Page 114 and 115: The Calendar 115"other point." In a
Page 116 and 117: CHAPTER SIXPROBABILITIESTHE serious
Page 118 and 119: Probabilities 119possibilities prod
Page 120 and 121: Probabilitiesl~lone suit will not b
Page 122 and 123: Probabilities 123into some one of w
Page 124 and 125: Probabilities 1~5Finally, the proba
Page 126 and 127: Probabilities 127It is clear that t
Page 128 and 129: Probabilities 129deck is usually no
Page 130 and 131: Probabilitiesunpartments, so that t
Page 132 and 133: Probabilities 133from the pieces. T
Page 134 and 135: x·whence ~ = S + g.Piwins, we must
Page 136 and 137: Probabilities 137with a throw of ta
Page 138 and 139: Probabilities 139do. Does there exi
Page 140 and 141: Probabilities 141staking .1 of what
Page 142 and 143: Magic Squares 143fore we can readil
Page 144 and 145: Magic Squares 145change of rows may
Page 146 and 147: Magic Squares 147b + h = c + g = d
Page 148 and 149: Magic Squares 149fill in the remain
Page 150 and 151: Magic Squares 15101-1 -1-1-1-1 "-1-
Page 152 and 153: Magic Squares 153in one-, two-, or
Page 154 and 155: Magic Squares 155We shall call the
Page 156 and 157: Magic Squares 157tinct in the modul
Page 158 and 159: Magic Squares 159shows how this met
Page 160 and 161:
that is,Magic Squaresb+p-Iu+p-1w ==
Page 162 and 163:
Magic Squares 163semimagic if t, u,
Page 164 and 165:
Magic Squares 16541, and 14. Hence
Page 166 and 167:
Magic Squares 167There are no regul
Page 168 and 169:
Magic Squares 169One can also borde
Page 170 and 171:
Magic Squares 171element of the giv
Page 172 and 173:
Magic Squares173113 124 119 126 1 1
Page 174 and 175:
Magic Squares 175possible to form a
Page 176 and 177:
Magic Squares 177square of order 12
Page 178 and 179:
Magic Squares 17912. EULER (GRAECO-
Page 180 and 181:
Magic Squares 181themselves must th
Page 182 and 183:
Magic Squares 183Figure 58. If (Fig
Page 184 and 185:
Magic Squares 185must take. You can
Page 186 and 187:
Magic Squares 187From this one can
Page 188 and 189:
Magic Squares 189number of distinct
Page 190 and 191:
Magic Squares 191We may remark in p
Page 192 and 193:
CHAPTER EIGHTGEOMETRIC RECREATIONS1
Page 194 and 195:
Geometric Recreations 1952. Dissect
Page 196 and 197:
Geometric Recreations 197SoZ1dion:
Page 198 and 199:
Geometric Recreations 1992. MOSAICS
Page 200 and 201:
Geometric Recreations~OlMosaic ofMo
Page 202 and 203:
Geometric Recreations111 1 1 3-+-+-
Page 204 and 205:
Geometric Recreations ~05have edges
Page 206 and 207:
Geometric Recreations 207solutions,
Page 208 and 209:
Geometric Recreations ~09the 20, an
Page 210 and 211:
Geometric Recreations ~11closed --
Page 212 and 213:
Geometric Recreations ~13example, s
Page 214 and 215:
Permutational Problems ~15child, ar
Page 216 and 217:
Permutational Problems 217the minor
Page 218 and 219:
Permutational Problems 219The two h
Page 220 and 221:
Permutational Problems 221Thus it t
Page 222 and 223:
Permutational ProblemsInitially the
Page 224 and 225:
Permutational Problemsget onto the
Page 226 and 227:
Permutational Problemseter give 2n
Page 228 and 229:
Permutational Problems 229go back t
Page 230 and 231:
Permutational Problems 231When two
Page 232 and 233:
Permutational ProblemaRn = nC2 = n(
Page 234 and 235:
Permutational Problems ~35n = 171,1
Page 236 and 237:
Permutational Problems 2371,2, 3, 4
Page 238 and 239:
The Problem of the Queens~391. THE
Page 240 and 241:
The Problem oj the Queens 241tions.
Page 242 and 243:
The Problem of the Queens ~43no sol
Page 244 and 245:
The Problem of the Queens 245Such a
Page 246 and 247:
The Problem of the Queens 247up int
Page 248 and 249:
The Problem of the Queens ~49FIGURE
Page 250 and 251:
The Problem of the Queens 251On the
Page 252 and 253:
The Problem of the Queens 253n-1 n-
Page 254 and 255:
The Problem of the Queens '255ular
Page 256 and 257:
CHAPTER ELEVENTHE PROBLEM OF THE KN
Page 258 and 259:
The Problem of the KnightU92. W ARN
Page 260 and 261:
The Problem of the Knight ~61tour i
Page 262 and 263:
The Problem of the Knight 263tal me
Page 264 and 265:
The Problem of the Knight265There a
Page 266 and 267:
CHAPTER TWELVEGAMES1. POSITIONAL GA
Page 268 and 269:
Games 269The checker man moves one
Page 270 and 271:
Games 271left," namely" no change."
Page 272 and 273:
Games 273U- 2 V-1 + u- 2 v + U-1V-2
Page 274 and 275:
Game8 275(16 moves for the 8 pawns
Page 276 and 277:
Games 277rules of play, or the piec
Page 278 and 279:
Games 279The centaur, which combine
Page 280 and 281:
Games 2816. REVERSI. This is played
Page 282 and 283:
Games 283tween 2 and 4 balls in eac
Page 284 and 285:
Games 285This great power granted t
Page 286 and 287:
Games ~87that White can always win,
Page 288 and 289:
Games 289if Black), the guide alone
Page 290 and 291:
Games 291Here are a few games. (W s
Page 292 and 293:
Games ~98units. The strength of a s
Page 294 and 295:
Games '295end of the game. When all
Page 296 and 297:
Games 297first one to be unable to
Page 298 and 299:
Games 299draw. In case of tie the o
Page 300 and 301:
Games 301in the original game, exce
Page 302 and 303:
Games 303initially the cubes are se
Page 304 and 305:
Games 805aspects of the theory of p
Page 306 and 307:
Games 307n (> 1) objects are even,
Page 308 and 309:
Games 309the two sets of pawns inte
Page 310 and 311:
Games 311Grasshopper is a variant o
Page 312 and 313:
Games 313one tries to construct squ
Page 314 and 315:
Games 315umn, one takes that opport
Page 316 and 317:
GamesRl Bl ~ B2 R3 B3 ~ B4~ B3 Rl B
Page 318 and 319:
Games 319cards by pairs in order an
Page 320 and 321:
Games 321up after the fifth deal in
Page 322 and 323:
Games 3~3of the cuts, we find that
Page 324 and 325:
THE FALSE COIN. 825Hence we can ide
Page 326 and 327:
Index 827Composite magic squares, 1
Page 328 and 329:
Needle problem, 132Negative digits,
show all

Mathematical_Recreations-Kraitchik-2e

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?