Quite simply, what is the value of <img src=/S/question.gif border=0 alt=question width=15 height=15>

If:

0 + 1 + 2 = 3

1 + 2 + 3 = 6

(0 X 1) + 2 = 7

(1 / 2) + (1 / 6) = 3

(3 + 6) - (2 + 1) = <img src=/S/question.gif border=0 alt=question width=15 height=15>

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">According to MY mad calculations, both 1 and 2 could be correct. If all intermediate results are to be integers, only 2 is correct. But perhaps there's an entirely different system to YOUR madness.</span hide>

Hans

There is a method to my madness which renders all the examples true. <img src=/S/crazy.gif border=0 alt=crazy width=15 height=15>
<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Your other assumptions are perfectly true which should lead you elsewhere for the solution.</span hide>

My method renders all examples true too, but I found two different solutions.

You've outpuzzled me Hans, for reasons which may become apparent if other loungers attempt the puzzle. <img src=/S/scream.gif border=0 alt=scream width=15 height=15>
Would you care to divulge your solutions to see if either resemble mine?

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">The mathematics must obviously be mad - either the numbers are not what you think they are or the operators aren't. I decided to take the operators + - x / at their face value and to treat the digits as symbols, or variables standing for other numbers. The only solution in which all numbers are single digits (although some of them are negative) is</span hide>

<table border=1><td><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">symbol</span hide></td><td><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">value</span hide></td><td align=right><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">0</span hide></td><td align=right><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">-4</span hide></td><td align=right><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">1</span hide></td><td align=right><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">2</span hide></td><td align=right><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">2</span hide></td><td align=right><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">3</span hide></td><td align=right><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">3</span hide></td><td align=right><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">1</span hide></td><td align=right><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">6</span hide></td><td align=right><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">6</span hide></td><td align=right><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">7</span hide></td><td align=right><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">-5</span hide></td></table>
<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">The calculations become
-4 + 2 + 3 = 1
2 + 3 + 1 = 6
(-4 x 2) + 3 = -5
(2 / 3) +( 2 / 6) = 1
(1 + 6) - (3 + 2) = 2
Translating the end result back to its symbol results in 1.

A solution where the divisions 1/2 and 1/6 result in whole numbers is</span hide>

<table border=1><td><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">symbol</span hide></td><td><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">value</span hide></td><td align=right><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">0</span hide></td><td align=right><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">6</span hide></td><td align=right><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">1</span hide></td><td align=right><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">-8</span hide></td><td align=right><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">2</span hide></td><td align=right><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">4</span hide></td><td align=right><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">3</span hide></td><td align=right><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">2</span hide></td><td align=right><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">6</span hide></td><td align=right><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">-2</span hide></td><td align=right><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">7</span hide></td><td align=right><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">-44</span hide></td></table>
<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">The calculations are

6 + -8 + 4 = 2
-8 + 4 + 2 = -2
(6 x -8) + 4 = -44
(-8 / 4) + (-8 / -2) = 2
(2 + -2) - (-8 + 4) = 4

and the end result translated back is 2.</span hide>

For once I concur but was too late to post my result.

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold"> I realised that the numbers were there to confuse so I replaced the numbers with letters and then did a bit of "number throwing" at your equations, eventually I got the samr results as Hans</span hide>

Hans and Jezza

Your solutions are not what I had in mind when constructing this puzzle. I thought I had all contingencies blocked and my awe has never been so struck at your ingenuity. Still, you have not given the answer to my puzzle. If I were to say:

3 X 4 = 6

Would your solution still be valid?

Perhaps a little clue (but not in the form of yet another incomprehensible "calculation") is in order to get us out of the rut we're in. TIA

It would, in the first case "4" would have a value of 6, which "6" would also have. So this makes it "iffy" (I assume only one symbol could 1 value)

In the second case, "4" would have a value of -1 to make it still valid.

But since you didn't specify 3X4 = 6 or give any indications of what is allowed or not, it makes it tougher for you to complain about "valid" responses that don't match your answer <img src=/S/grin.gif border=0 alt=grin width=15 height=15>

Steve

The mathematics must obviously be mad - either the numbers are not what you think they are........... Hans

I realised that the numbers were there to confuse so I replaced the numbers with letters.............Jezza

Incomprehensible? - Moi?

Methinks you think too much! <img src=/S/grin.gif border=0 alt=grin width=15 height=15>

I thought I'd created a simple, uncontroversial puzzle but the best laid plans of mice and Alf....

Here's the key to my solution:

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">4 X 4 = 7</span hide>
<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Four X Four = Sixteen</span hide>

Quite right, and so modest. <img src=/S/grin.gif border=0 alt=grin width=15 height=15>

<img src=/S/thumbup.gif border=0 alt=thumbup width=15 height=15> <img src=/S/cool.gif border=0 alt=cool width=15 height=15> Now that's a good puzzle and I like it! I just wish I would've solved it. A+ for uniqueness.