SOLUTION: ​The five digits of the base 5 numeration system were assigned letters from the set {V, W, X, Y, Z}, not necessarily in the order from 0 – 4. If three consecutive integers in

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Question 1114339: ​The five digits of the base 5 numeration system were assigned letters from the set {V, W, X, Y, Z}, not necessarily in the order from 0 – 4. If three consecutive integers in increasing order are encoded as VYZ, VYX, and VVW, respectively, what is the base 10 expression for the integer coded as XYZ?
Answer by Edwin McCravy(20062)   (Show Source): You can put this solution on YOUR website!
Since VYZ, VYX, and VVW are consecutive integers, these
additions of 1 must be true.

VYZ     VYX
 +1      +1
VYX     VVW

From the addition on the left we see that Z+1=X for nothing was
carried, since digits V and Y stayed the same when 1 was added

From the addition on the right, 1 must be carried to the middle
column of digits; for otherwise, the middle V in VVW would have
been Y.  Since these are consecutive integers, and this
is the first time there was 1 to carry, X must be the 
largest digit X=4, and W=0. And since Z+1=X, Z=X-1=4-1=3. So the 
above two additions are now

         1
VY3     VY4
 +1      +1
VY4     VV0

The only two digits that haven't been used are 1 and 2.
From the second addition we see from the middle column that V 
must be larger than Y, so Y=1 and V=2.  So the additions are

213     214
 +1      +1
214     220

The question is:

what is the base 10 expression for the integer coded as XYZ?

"XYZ" = 25X+5Y+Z = 25(4)+5(1)+3 = 100+5+3 = 108.

Edwin
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