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[...]... the numbers 23 and 28 Modern psychoanalysts, beginning with Sigmund Freud and Wilhelm Fliess, believe these numbers "bar and separate" men from women The first is the length of the ideal male cycle and the second the length of the ideal female cycle They see great significance in these two numbers, since all possible integers can be generated from them For example, the number 13 equals (3 X 23) + (-2... they were commonplace in England's banking system If an individual made a loan to a bank, the amount of the loan was etched onto a stick, and the stick was split laterally to create two copies The one held by the bank was called a "foil," and the one held by the individual making the loan was called a "stock"; hence, the individual was a "stockholder." When the loan was called, the stock was "checked"... Moreover, the skull bones were thick approximately the thickness of Neanderthal skulls On the other hand, Ishango man did not have the overhanging brow of Neanderthal and other earlier forms his chin was shaped like the chin of modern man the long bones of his body were quite slender this adds up to a unique picture No other fossil man shows such a combination Figure 1 The Ishango bone (Reprinted... groups Along one column there are 11, 21, 19, and 9 notches Along another there are eight groups of 3, 6, 4, 8, 10, 5, 5, and 7 notches Along the third column there are 11, 13, 17, and 19 notches "I find it difficult to believe," de Heinzelin continues, "that these sequences are nothing more than a random selection of numbers." Indeed not We may have in Figure 1 the earliest number system possible, and. .. example, in central Brazil the Bakairi have words for only "one" and "two." To count higher they must combine these words Thus, one is tokale, two is ahdge, and three is ahdge tokdle Four, of course, is ahcige ahcige Five and six follow logically, but for seven there is no word at all We might expect ahdge ahdge ahige tokaile (meaning 2 + 2 + 2 + 1), but such a phrase requires the listener (and the speaker)... 3923 3929 5659 5669 5683 568R9 56 57 58 59 60 353 359 367 373 379 308 3 308 9 3109 3119 3121 4799 4801 4813 4817 4831 55 71 72 73 74 1 523 229) 1531 2297 1543 2309 1549 2311 105532335 3963 4721 3877 4723 4729 3889 4733 3907 4751 2339 3931 5137 3943 2341 31 63 23147 3167 3947 3967 3169 2357 3181 3989 807 907 63 303 7 304 1 304 9 306 1 306 7 307 0 1 559 1567 1571 1579 1 583 199 211 273 1227 229 233 739 241 251... ago -and possibly much longer-a tiny fishing village flourished around Lake Edward in Zaire, situated in central Africa The people of the village are now called the Ishango The evidence that can be excavated around the lake suggests that the Ishango practiced cannibalism, as did others at the time, and built certain crude tools, mostly used for fishing, hunting, and gathering They are our intellectual... what might be called the "psychoanalytic barricading." This is not the the two sides of the rectangle be x and y Then x *y= 2x + 2y A little algebra changes this toy = 2 + 4/(x- 2) Now if y is to be an integer, as is called for in the problem, then (x-2) must be a divisor of 4, otherwise the right side of the equation is 2 plus "some fraction." This means (x-2) must be either 1, 2, or 4, and we have only... he etches in 3, and doubles it to 6 Then 4, and 8 Or is this another coincidence? THE FIRST The third side of the bone is a little more confusing The notches this time are 11, 13, 17, and 19 These are all the prime numbersnumbers that can be divided only by themselves and one-between ten and twenty Again, is this a coincidence? De Heinzelin believes the bone represents "an arithmetical game of some... several volumes this way, but by necessity I have had to pick my way through several fascinating examples I've tried to sample much of the world across several centuries Starting with Africa and China is unavoidable Including yet another chapter on magic squares may seem like overkill to some but not to others, and perhaps the history will be interesting to everyone After that I pass to Europe and the . class="bi x0 y0 w0 h0" alt="" K"CitenZ? ptwz=zA,-cs (I * w Ce 'loc l a Az tcI CLAiSIC BRAINTEASERS AND OTHER TIMELESS MATHEMATICAL GAMES OF THE LAST 1 0 CENTURIES Dominic. merely random, has always been hard to swallow, since primes are a fairly advanced concept. But fundamental concepts quite often are the ones that first arise to the novice,. . approximately the thickness of Neanderthal skulls On the other hand, Ishango man did not have the overhanging brow of Neanderthal and other earlier forms . . . his chin