I need help with some brainteasers!

Factual Questions
1

I’ve got some brainteasers I’m trying to solve. I’ve got most of them, but these I can’t seem to figure out:

How can the following be true:
A = 3
B = 4

But A + B = 5

I’m thinking for this one either something like different values of A and B are being used, or the statement simply can’t be true.

How can you, with one line, turn VII into the number 8?

Is there some trick to this other than adding another line and making it VIII?

Separate all nine dots into their own individual squares by drawing two squares.

. . .
. . .
. . .
Those dots are the pattern that is given.
So can anyone give me hand with these please?

2

I’m thinking the symbol 5 must stand for the number 7, but i can’t work out the framework in which this might be true.

3

For #1, A and B are vectors; A=3x, B=5y; the length of their sum is then 5

#2 seems a little too obvious, but your answer works, so why should there be a less obvious one?

For #3, are you sure you have to draw squares? with 2 rectangles you can do it; I don’t think it’s possible by drowing squares.

4

The first could also be something like A = two (3 letters), B = five (4 letters), A + B = seven (5 letters). I admit, it’s a little stretched :wink:

5

Yeah, I guess number 2 is obvious. I guess I’m just paranoid. As for 3, yep, squares it is. Now I’m going to go look up stuff about vectors from number 1, because I have no idea about them!

6

#1 could also use somewhat esoteric set theory. If “=” represents “has a cardinality of” and “+” represents “union”, then { a, b, c } for A and { b, c, d, e } for B would fit the bill.

In #3, are the dots supposed to be arranged in a square? Because as viking hints, that makes a difference.

7

Well damn. One of my math classes last year had all that cardinality and union stuff in it and I didn’t even think about it looking at the problem! So its either that, vector math, or The Weak Force’s theory…

8

For number three, you can only separate them into nine squares if you’re using rectangles. You can separate them into nine triangles using two squares, though.

9

I think you just make one of the squares rotate 45 degrees

10

Damn sock munkey beat me to it. #3 will look like this:



   ^
 ./.\.
 / _ \ 
/.|.|.\
\  -  /
.\ . /.
  \ /
   v

the two squares should touch at the four corners of the middle square, but thats the idea.

11

=)

12

but then the dots wouldn’t be in squares, but triangles.

13

#1 – Vectors? Why complicate it? The numbers plug into the Pythagorean theorem quite nicely, describing the lengths of the sides of a right triangle. Where C = the length of the hypotenuse, A^2 + B^2 = C^2. Thus, if A=3 and B=4, then C=5 every time. Carpenters use this all the time to lay out walls that are square; it works equally well with multiples, like A=12, B=16, C=25. Custom countertop makers will still ask for the ‘C’ measurement so they can cut a proper miter joint.

#2 – Pretty obvious; again, why complicate it?

#3 – I’ll wait for a better layout of the puzzle. The ASCII version isn’t up to snuff.