HDD Killers

There was a program on the TV about a kid who is incredibly gifted, I think he’s about 12 years old and he’s trying to find a cure for cancer and is doing a medical degree or something, I wasn’t really all that interested. Anyway, his IQ is thought to be greater than Einstein’s, so I hit google to find Einstein’s IQ. Turns out that he never actually took an IQ test, so no-one really knows his IQ for certain, it’s all just guess-work. Anyway, the only reason I mention this is because it led me to the “Einstein I.Q. Test“, and everyone loves a good back-story.

I should mention at this point that if you plan to take the test, do so before reading on as I will discuss one question and it’s answer.

Here’s some text to put a gap between the warning and an answer to one of the questions, because seriously, it’s coming up in the next few lines. Look away now, quick, come on, you’re almost out of text, look away dammit. Fine, sod you then.

So yeah, I disagree with the answer to question 4. Here’s question 4:

A cube is made of a white material, but the exterior is painted black. If the cube is cut into 125 smaller cubes of exactly the same size, how many of the cubes will have 2 of their sides painted black?

And here’s the supposed answer:

44. 36 of the cubes have EXACTLY 2 of their sides painted black, but because a cube with 3 of its sides painted black has 2 of its sides painted black, you must also include the corner cubes. This was a trick question, but hopefully the title of the puzzle tipped you off to this.

When I first thought about the answer to this quesion I considered including cubes with three sides painted black, but then I read the question again, “how many of the cubes will have 2 of their sides painted black?” Well obviously cubes with three of their sides painted black will have at least two of their sides painted black, but they will not have only two sides painted black, and the question specifically states 2 sides, no more, no less. Perhaps if I write this in code it will be easier to understand, this is what the question asks:

if( black_sides == 2 ){ count++; }

This is what the answer implies the question meant:

if( black_sides >= 2 ){ count++; }

The first condition is an equality test, the second is an inequality test. There’s a subtle difference there, but it makes a big difference to the answer. I actually thought that this was one of the “tricks” mentioned at the start. Well there was a “trick” there, but it was requiring the user to infer something that was not explicitely stated in the question instead of taking the question at face value. To me it seems as though the question was badly worded, and deliberately so, resulting in the meaning being ambiguous. Therefore it’s possible to think about this question all you want and consider different interpretations and meanings, but at the end of it you’re left with only a 50/50 chance of getting the “correct” answer (unless you went and calculated it completely wrong no matter which interpretation you took).

Here is an alternative question with the same meaning as the one that was asked. How many of the cubes will have 4 of their sides painted white? If you try to answer this question in the same way intended as the original question, you could include cubes which have 4, 5 or 6 of their sides painted white (and therefore 2, 1 or 0 of their sides painted black), even though the two questions are actually the same. You’d end up with the answer 117, very different indeed to the 44 they were looking for, yet the two questions are identical.

Anyway, I got 6 / 10 correct, the four that I got wrong were 3, 6, 10 and, of course, 4. How did you fare?