The letters of TALES have been added to the grid to form six words, one being a lingual import into English.
| L |
E |
A |
S |
T |
| S |
L |
A |
T |
E |
| S |
T |
A |
L |
E |
| S |
T |
E |
A |
L |
| T |
A |
E |
L |
S |
| T |
A |
L |
E |
S |
Assign a base 10 digit to each of the letters in the grid to create an alphametic so that each row but one forms a 5-digit prime number.
This situation can occur in three ways, and logic should prevail.
5 dim Used(9),Pv(6)
10 for L=1 to 9
15 Used(L)=1
20 for S=1 to 9 step 2
30 if Used(S)=0 then
35 :Used(S)=1
40 :for T=1 to 9
42 :if Used(T)=0 then
44 :Used(T)=1
50 :for A=0 to 9
52 :if Used(A)=0 then
54 :Used(A)=1
56 :for E=1 to 9 step 2
60 :if Used(E)=0 then
70 :Used(E)=1
75 :Least=L*10000+E*1000+A*100+S*10+T
76 :Slate=S*10000+L*1000+A*100+T*10+E
77 :Stale=S*10000+T*1000+A*100+L*10+E
78 :Steal=S*10000+T*1000+E*100+A*10+L
79 :Taels=T*10000+A*1000+E*100+L*10+S
80 :Tales=T*10000+A*1000+L*100+E*10+S
81 :Prmcnt=0:for I=1 to 6:Pv(I)=0:next
82 :if prmdiv(Least)=Least then Prmcnt=Prmcnt+1:Pv(1)=1:endif
83 :if prmdiv(Slate)=Slate then Prmcnt=Prmcnt+1:Pv(2)=1:endif
84 :if prmdiv(Stale)=Stale then Prmcnt=Prmcnt+1:Pv(3)=1:endif
85 :if prmdiv(Steal)=Steal then Prmcnt=Prmcnt+1:Pv(4)=1:endif
86 :if prmdiv(Taels)=Taels then Prmcnt=Prmcnt+1:Pv(5)=1:endif
87 :if prmdiv(Tales)=Tales then Prmcnt=Prmcnt+1:Pv(6)=1:endif
88 :if Prmcnt>4 then
89 :print:print Least;Pv(1):print Slate;Pv(2):print Stale;Pv(3):pr
int Steal;Pv(4):print Taels;Pv(5):print Tales;Pv(6):print Prmcnt:Sct=Sct+1
90 :endif
91 :Used(E)=0
92 :endif
93 :next E
94 :Used(A)=0
95 :endif
96 :next A
97 :Used(T)=0
98 :endif
99 :next T
100 :Used(S)=0
110 :endif
120 next S
125 Used(L)=0
130 next L
150 print Sct
finds nine solutions:
37612 0
13627 1
12637 1
12763 1
26731 1
26371 1
5
41539 1
34591 1
39541 1
39154 0
95143 1
95413 1
5
51439 1
35491 1
39451 1
39145 0
94153 1
94513 1
5
53791 1
95713 1
91753 1
91375 0
17359 1
17539 1
5
79813 1
17839 1
13879 1
13987 0
38971 1
38791 1
5
73019 1
17093 1
19073 1
19307 0
90371 1
90731 1
5
79031 1
37019 1
31079 1
31907 1
10973 1
10793 0
5
87613 1
18637 1
13687 1
13768 0
36781 1
36871 1
5
97213 1
19237 1
13297 1
13729 1
32791 0
32971 1
5
9
The 1 or 0 next to each line indicates whether the number is or is not, respectively, a prime number.
So if there are nine solutions, what are the "three ways"?
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Posted by Charlie
on 2010-03-20 13:59:49 |
computer solution
