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A287219 The numbers which are of the form (a*100 + b*10 + c)*(d*10 + e) = (f*10 + g)*(h*10 + i) (a, b, ... , i are nine digits, 1, 2, ... , 9). 0

%I

%S 3634,3726,3886,4002,4234,4662,5022,5056,5568,7008,7448

%N The numbers which are of the form (a*100 + b*10 + c)*(d*10 + e) = (f*10 + g)*(h*10 + i) (a, b, ... , i are nine digits, 1, 2, ... , 9).

%C Dudeney asked the largest number in 1917 and 7448 (= 532 * 14 = 98 * 76) was found in 1971.

%D Henry Ernest Dudeney, Amusements in Mathematics, 1917.

%e Dudeney gave the following example.

%e 158 * 23 = 79 * 46 (= 3634),

%e 158 * 32 = 79 * 64 (= 5056),

%e 174 * 32 = 96 * 58 (= 5568).

%t Reap[Do[{a, b, c, d, e, f, g, h, i} = p; m = (a*100 + b*10 + c)*(d*10 + e); If[m == (f*10 + g)*(h*10 + i), Print[m]; Sow[m]], {p, Permutations[ Range[9]]}]][[2, 1]] // Union (* _Jean-Fran├žois Alcover_, May 22 2017 *)

%o (Ruby)

%o ary = []

%o (1..9).to_a.permutation{|a|

%o i = a[0] * 100 + a[1] * 10 + a[2]

%o j = a[3] * 10 + a[4]

%o k = a[5] * 10 + a[6]

%o l = a[7] * 10 + a[8]

%o ary << i * j if i * j == k * l

%o }

%o p ary.uniq.sort

%K nonn,base,fini,full

%O 1,1

%A _Seiichi Manyama_, May 22 2017

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Last modified January 22 23:50 EST 2022. Contains 350504 sequences. (Running on oeis4.)