Substitute each of the capital letters in bold by a different decimal digit from 1 to 9 and determine the minimum positive integer value that the following cryptarithmetic expression can assume.

(A/B)^C + (D/E)^F + (G/H)^I

How about the maximum positive integer value that this expression can assume?

135 distinct integer values can be formed from the expression (A/B)^C + (D/E)^F + (G/H)^I where each capital letter in bold represents a different decimal digit from 1 to 9:

70, 132, 241, 356, 374, 407, 435, 593, 665, 672, 810,
882, 889, 1098, 1100, 2222, 2255, 2276, 2283, 2432,
2824, 2942, 2948, 3937, 4154, 4507, 6526, 6740, 6908,
7307, 7713, 7913, 9205, 9373, 9772, 9967, 10219, 14465,
15762, 16880, 17323, 17346, 17521, 17540, 17575, 17738,
17792, 17816, 17920, 17923, 18068, 18137, 19936, 20054,
20058, 20723, 20984, 21902, 22314, 22977, 23188, 23432,
23449, 24241, 32090, 33408, 33625, 35019, 35036, 36498,
59181, 59204, 59433, 61244, 67966, 75449, 78198, 78641,
78664, 78858, 78893, 79110, 82302, 84750, 84767, 97816,
117690, 117896, 118148, 118754, 124242, 262515, 262897,
263296, 264363, 264577, 278560, 278967, 279977, 280183,
280435, 281041, 286529, 340285, 391265, 391482, 392876,
392893, 1679987, 1681835, 1953257, 1953280, 1953509,
1955320, 1969525, 2097459, 2097476, 2097696, 2097913,
4783005, 4783028, 4783220, 4783257, 4784009, 5765108,
5765125, 5765345, 5765562, 40353643, 40353666, 40353858,
40353895, 40354647, 43046881, and 134217888

(5/9)¹ + (7/3)² + (8/4)⁶ = 70
(6/2)¹ + (9/3)⁵ + (8/4)⁷ = 134217888, and
(9/3)¹ + (6/2)⁵ + (8/4)⁷ = 134217888

Posted by Dej Mar on 2009-02-09 17:33:10