000RM.dvi
13.4 The most popular Monthly problem 407 13.4 The most popular Monthly problem The following problem, E 1111, is said to be the ...
408 Digit problems 13.5 The problem of 4n’s 1=nn++nn 2=nn+nn 3=n+nn+n 4=.nn−+..nn 5=.nn++..nn 6= (n+n+n n ) ! 7=n−..nn−.n 8=.nn− ...
13.5 The problem of 4n’s 409 Appendix: Squares with 9 distinct nonzero digits 11826 139854276 12363 152843769 12543 157326849 14 ...
410 Digit problems Exercise 1.Lucky Larry, a mathematics student whose plausible mistakes in computation always results in corre ...
13.5 The problem of 4n’s 411 10.Here are seven consecutive squares for each of which its decimal digits sum to a square: 81 , 10 ...
412 Digit problems Charles Twigg’s square number trivia What three-digit squares have the following characteristics? 1.are palin ...
13.5 The problem of 4n’s 413 Cross number puzzle Place 13 three - digit square numbers in the spaces in the accompanying grid. ( ...
414 Digit problems Project Arrange the ten digits (0, 1,..., 9, norepetition) in a row abcdef ghij so that the following 3-digit ...
Chapter 14 Numbers with many repeating digits 1 A quick multiplication 2 The repunits 3 Squares of repdigits 4 Sorted numbers wi ...
416 Numbers with many repeating digits 14.1 A quick multiplication.................. What is the smallest positive integer with ...
14.2 The repunits 417 14.2 The repunits .................. The repunitRnis the number whose decimal representation consists of a ...
418 Numbers with many repeating digits 14.3 Squares of repdigits .................. In the decimal representations of integers, ...
14.4 Sorted numbers with sorted squares 419 14.4 Sorted numbers with sorted squares ........... A number issortedif its digits a ...
420 Numbers with many repeating digits Appendix: Factorization of 10 n+1for 1 ≤n≤ 50 n Factorization of 10n+1 111 2101 37 × 11 × ...
14.4 Sorted numbers with sorted squares 421 Exercise 1.Show that (^16) n (^6) n 4 = 1 4 , (^19) n (^9) n 5 = 1 5 , (^26) n (^6) ...
422 Numbers with many repeating digits ...
Chapter 15 Digital sum and digital root 1 Digital sum sequences 2 Digital root 3 Digital roots of the powers of 2 4 Digital root ...
424 Digital sum and digital root 15.1 Digital sum sequences .................. The digital sum of a positive integernis the sum ...
15.2 Digital root 425 15.2 Digital root .................. Given a positive integern, letd(n)be the sum of the digits ofn. If th ...
426 Digital sum and digital root 15.3 The digital roots of the powers of 2 ........... n 0123 4 5 6 2 n 1248163264 D(2n)1248 7 5 ...
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