Courses/CS 460/Fall 2005/Homework/Joey Leung/Nov 12

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[edit] Pick two puzzles from FreePuzzles.com

[edit] Math002 - A to I are 1 to 9

  AB
X  C
----
  DE
+ FG
----
  HI

Every alphabet represents a different digit from 1 to 9 to make the calculation. What are they?


local     
   proc {Math002 Solution}
      A B C D E F G H I
      Vars = [A B C D E F G H I]
   in
      Solution = [A B C D E F G H I]
      Vars ::: 1#9
      (10*A + B) * C =: (D*10 + E)
      (D*10 + E) + (F*10 + G) =: (H*10 + I)
      {FD.distribute ff Vars}
      {FD.distinct Vars}
   end
in
   {Browse {SearchAll Math002}}
end


[edit] Math003 - A strange 5 digit number


  1ABCDE
X      3
--------
  ABCDE1  	 

A five digit number is represented by ABCDE. If we add the number 1 in front of ABCDE, 
then times 3, the result number will be ABCDE appended by the number 1 (as shown in the figure). 
What is this five digit number?



local     
   proc {Math003 Solution}
      A B C D E 
      Vars = [A B C D E]
   in
      Solution = [A B C D E]
      Vars ::: 1#9
      (100000 + A*10000 + B*1000 + C*100 + D*10 + E) * 3
      =: (A*100000 + B*10000 + C*1000 + D*100 + E*10 + 1)
      {FD.distribute ff Vars}
      {FD.distinct Vars}
   end
in
   {Browse {SearchAll Math003}}
end


[edit] Math024 - Reverse the digit sequence by multuplying 7


   ABCD
X     7
-------
  EDCBA

What a magic number 7 is! It can reverse the digit sequence of a 4 digit number. 
A, B, C, D and E are distinct single digit numbers. What is the 4 digit number ABCD?



local     
   proc {Math024 Solution}
      A B C D E 
      Vars = [A B C D E]
   in
      Solution = [A B C D E]
      Vars ::: 1#9
      (A*1000 + B*100 + C*10 + D) * 7
      =: (E*10000 + D*1000 + C*100 + B*10 + A)
      {FD.distribute ff Vars}
      {FD.distinct Vars}
   end
in
   {Browse {SearchAll Math024}}
end


[edit] Math035 - From 1 to 9 to make a multiplication


   ****
X     *
-------
   ****

Fill in the boxes with 1, 2, 3, 4, 5, 6, 7, 8, and 9 to make the multiplication equation work.



local     
   proc {Math035 Solution}
      A B C D E F G H I
      Vars = [A B C D E F G H I]
   in
      Solution = [A B C D]#[E]#[ F G H I]
      Vars ::: 1#9
      (A*1000 + B*100 + C*10 + D) * E
      =: (F*1000 + G*100 + H*10 + I)
      {FD.distribute ff Vars}
      {FD.distinct Vars}
   end
in
   {Browse {SearchAll Math035}}
end


[edit] Math065 - All prime numbers multiplication

Does not work, it returns a "nil". 


    ***
X    **
-------
   ****
  ****
-------
  *****

Can you fill in only prime number digits in the boxes to make this equation possible? 
It really means that you can only use number 2, 3, 5 nad 7 in the boxes.



local     
   proc {Math065 Solution}
      A B C D E F G H I J K L M N O P Q R
      Vars = [A B C D E F G H I J K L M N O P Q R]
   in
      Solution = [A B C]#[D E]#[F G H I]#[J K L M]#[N O P Q R]
      Vars ::: {fun {$} choice 2 []3 []5 []7 end end}
      %Vars ::: choice 2 []3 []5 []7 end
      %Vars ::: 2
      %Vars ::: 3
      %Vars ::: 5
      %Vars ::: 7
      (A*100 + B*10 + C) * E =: (F*1000 + G*100 + H*10 + I)
      (A*100 + B*10 + C) * (D*10) =: (J*10000 + K*1000 + L*100 + M*10)
      (F*1000 + G*100 + H*10 + I) + (J*10000 + K*1000 + L*100 + M*10)
      =: (N*10000 + O*1000 + P*100 + Q*10 + R)
      {FD.distribute ff Vars}
   end
in
   {Browse {SearchAll Math065}}
end


[edit] DigitsToInt that uses FoldR


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