If the days of the week are represented as follows:
MO TU W TH F SA SU
and are numbered 1 to 7 as follows:
MO TU W TH F SA SU
1 2 3 4 5 6 7
assign to each letter a nonzero digit so that the numbers represented by the day abbreviations given are each divisible by the digit assigned to that day, but by no higher digit.
From the givens, the cryptorithmic value of each day abbreviation numbered as d is equal to d*p, such that p is either 1 or a prime p > d. Thus, Wednesday [W] and Friday [F], as single cryptorithmic digits are 3 and 5 respectively. Further, p is not equal to 11 as both digits of the two digit number, d*p, would otherwise be the same; and p is not equal to 5 when d is even as the second digit would otherwise be 0. From further processes of elimination, noting Saturday [SA] and Sunday [SU] share the 'digit' S, Tuesday [TU] and Thursday [TH] share the 'digit' T, and Sunday [SU] and Tuesday [TU] share the 'digit' U, it can be deduced that {1,2,3,4,5,6,7,8,9} = {S,A,W,U,F,H,T,M,O}.
MO = 89; (89/1 = 89)
TU = 74; (74/2 = 37)
W = 3; ( 3/3 = 1)
TH = 76; (76/4 = 19)
F = 5; ( 5/5 = 1)
SA = 12; (12/6 = 2)
SU = 14; (14/7 = 2)
Edited on February 18, 2010, 3:47 am

Posted by Dej Mar
on 20100218 03:40:26 