Question

Today I had an interview for a developer job and I had to do this aptitude test…
I got stuck one 2 questions:

box 1  box 2  box 3
 A      B      C

How to put A in each boxes with only those 4 operator (ADD, SUB,MULT and DIV)?

box 1  box 2  box 3

You have the numbers 1,2 and 3 that can be in either box1 box2 or box3 but we don’t know in which is which… How to put 7 in box 3 ?

Can someone can explain me how to do it ?
ps: syntax is: ADD,1,2,3 => box3 = box1 + box2

Thank you

Answer 1

For the first question, you can set boxes B and C equal to 2A by just storing A + A in each:

ADD 2, 1, 1
ADD 3, 1, 1

Now, just subtract A from each box:

SUB 2, 2, 1
SUB 3, 3, 1

This results in A stored everywhere. The resulting program is thus

ADD 2, 1, 1  // Box 1 = A  Box 2 = 2A  Box 3 = C
ADD 3, 1, 1  // Box 1 = A  Box 2 = 2A  Box 3 = 2A
SUB 2, 2, 1  // Box 1 = A  Box 2 = A   Box 3 = 2A
SUB 3, 3, 1  // Box 1 = A  Box 2 = A   Box 3 = A

For the second question, one cute trick would be to divide some box by its own value to put 1 into it. For example:

DIV 1, 1, 1

Now, let’s put 2 into box 2 by doubling the contents of box 1 and storing it there:

ADD 2, 1, 1

Now, let’s put 4 into box 3 by doubling the contents of box 2 and storing it there:

ADD 3, 2, 2

Next, add 2 to box three by adding in the contents of box 3. This makes box 3 hold 6:

ADD 3, 3, 2

Finally, add 1 to box three by adding in the contents of box 3. This makes box 3 holds 7:

ADD 3, 3, 1

The total program is thus

DIV 1, 1, 1   // Box 1 = 1  Box 2 = ?  Box 3 = ?
ADD 2, 1, 1   // Box 1 = 1  Box 2 = 2  Box 3 = ?
ADD 3, 2, 2   // Box 1 = 1  Box 2 = 2  Box 3 = 4
ADD 3, 3, 2   // Box 1 = 1  Box 2 = 2  Box 3 = 6
ADD 3, 3, 1   // Box 1 = 1  Box 2 = 2  Box 3 = 7

Hope this helps!