000RM.dvi
15.4 Digital root sequences 427 15.4 Digital root sequences.................. A digit root sequence(an)is defined recursively by ...
428 Digital sum and digital root Exercise 1.A Filzian number is one which is the product of its digits and digial sum. For examp ...
15.4 Digital root sequences 429 Project: Sum of squares of digits Letf(n)be sum of the digits ofn. For example,f(1) = 1,f(2) = 4 ...
430 Digital sum and digital root ...
Chapter 16 3-4-5 triangles in the square ...
432 3-4-5 triangles in the square ...
433 ...
434 3-4-5 triangles in the square θ tanθ= 1 φ . ...
435 Exercise 1.Show that the shaded triangle is a 3:4:5 triangle. 2.Find the ratio of the areas ofABY,BCXY, andAXD. A B D X C Y ...
Chapter 17 Combinatorial games 1 Subtraction games 2 The nim sum 2 Nim 3 Northcott’s variation of nim 4 Wythoff’s game Appendix: ...
502 Combinatorial games 17.1 Subtraction games .................. Starting with a given positive integerN, two players alternate ...
17.1 Subtraction games 503 17.1.1 The Sprague-Grundy sequence LetGbe a 2-person counter game in which two players alternately re ...
504 Combinatorial games 17.1.2 Subtraction of square numbers Two players alternately subtract a positive square number. We calcu ...
17.1 Subtraction games 505 17.1.3 Subtraction of square numbers The first 100 terms of the Sprague-Grundy sequence are 123456789 ...
506 Combinatorial games Subtraction of aliquot parts Two players start with a positive integer and alternately subtract any aliq ...
17.1 Subtraction games 507 Subtraction of proper divisors The rules are the same with the exception that onlyproperdivisors may ...
508 Combinatorial games Subtraction of primes The first 100 terms of the Sprague-Grundy sequence 12345678910 0011223340 01122334 ...
17.2 The nim sum of natural numbers 509 17.2 The nim sum of natural numbers ........... The nim sum of two nonnegative integers ...
510 Combinatorial games 17.3 The gameNim ...................... Given three piles of marbles, witha,b,cmarbles respectively, pla ...
17.4 Northcott’s variation of Nim 511 17.4 Northcott’s variation of Nim ........... Two players alternately move their counters ...
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