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The overall possibilities for the solution are:
ZWEI DREI VIER
2053 1653 4356
2753 1653 4356
2953 1653 4356
7253 1653 4356
7853 1653 4356
8053 1653 4356
8753 1653 4356
All agree that DREI = 1653 and VIER = 4356.
Bonus:
The only ZWEI that becomes unique upon being told the value of Z and that there are no zeros, is 8753.
5 dim Taken(9)
10 for Z=1 to 9
20 Taken(Z)=1
30 for W=0 to 9
40 if Taken(W)=0 then
50 :Taken(W)=1
60 :for E=0 to 9
70 :if Taken(E)=0 then
80 :Taken(E)=1
90 :for I=0 to 9
100 :if Taken(I)=0 then
110 :Taken(I)=1
120 :for D=1 to 9
130 :if Taken(D)=0 then
140 :Taken(D)=1
150 :for R=0 to 9
160 :if Taken(R)=0 then
170 :Taken(R)=1
180 :for V=1 to 9
190 :if Taken(V)=0 then
200 :Taken(V)=1
210 :Zwei=1000*Z+100*W+10*E+I
220 :Drei=1000*D+100*R+10*E+I
230 :Vier=1000*V+100*I+10*E+R
240 :TrNo=int(sqrt(2*Drei))
250 :Sr=int(sqrt(Vier)+0.5)
260 :if prmdiv(Zwei)=Zwei and TrNo*(TrNo+1)/2=Drei and Sr*Sr=Vier then
270 :print Zwei,Drei,Vier
280 :endif
285 :Taken(V)=0
290 :endif
300 :next V
305 :Taken(R)=0
310 :endif
320 :next R
325 :Taken(D)=0
330 :endif
340 :next D
345 :Taken(I)=0
350 :endif
360 :next I
365 :Taken(E)=0
370 :endif
380 :next E
385 :Taken(W)=0
390 :endif
400 next W
405 Taken(Z)=0
410 next Z
From Enigma No. 1445 by Richard England, New Scientist, 2 June 2007. |
