Clutch

Yeah, my question. I considered

(s(0)+s(0)+s(0)+s(0))!

where s is the successor function.

But that seemed like cheating, or, at least, not the answer being fished for.

Farren

My point is, where does anyone else get the 1 required to specify that they are using a base 10 number system when representing the problem in base 10 notation?

If they don't, they can say

(cos(0) + cos(0) + cos(0) + cos(0))! = 24

and I can say

Wrong.

Because in hex

(cos(0) + cos(0) + cos(0) + cos(0))! = 18

What I'm trying to get across is saying

"This column is 2^0 and this column is 2^1 and this column... and this column is the negative sign"

is no different from saying

"This column is 10^0 and this column is 10^1 and..."

Note that in the above statement, 8 does not appear and 2 appears in the same context as 10.

If you disallow the one, you disallow the other, and all solutions are made illegal by the same reasoning.

Just as you can assume, when writing the solution that the default notation is implicitly base 10, I can equally assume when performing binary computations to achieve the solution is implicitly provided in 8-bit, 2's-complement notation.

Farren

In fact all operators are functions. While some (like the arithmetic operators, are ubiquitous, none are more "true" or "valid" than others (see my posts about Turing Machines)

The reverse polish notation used by HP calculators demonstrates this explicitly

+(1,1) = 2

Clutch

I once heard a mathematician tell a physicist during a question period: "I can tell why you multiply that value by ten. It's because that's how many fingers you have."

Clutch

The question was which functions are to be considered "mathematical operators" for the purposes of this puzzle. My suspicion was that the successor function would be a cheat.

Farren

...and the answer would conclusively be "Yes". Any function that can be described by a Turing Machine is a mathematical function/operator, but I don't think that's what the framers of the puzzle intended

stretch

If you consider 'rounding to the nearest integer' to be a 'mathematical operation'

then [rounded(arccos(-cos(0)))]^[rounded(arccos(-cos(0)))] - [rounded(arccos(-cos(0)))] = 24, and only uses three zeros.

(where ^ indicates 'raised to the power' )

If I was being more careful, maybe I would use the absolute value of arccos(-1).

HeatherD

You guys are taking this way too seriously! Over at the Physics forum, where I found this, there was hardly any discussion. A number of people didn't know about factorials (an odd surprise given it is a physics forum) but no one seemed to argue about the things you guys do.

I should mention that where they have the brain teasers, once someone answers it, the thread is locked. Discussion is left to another forum, depending on the type of teaser.

I think it was assumed that the numbers were in base 10, as is customary when there is no base indicator.

Φ

Loren Pechtel

Agreed--I had always thought 0! was undefined. Your math seems sound and my calculator comes up with 1, also.

Loren Pechtel

Originally posted by Farren
My point is, where does anyone else get the 1 required to specify that they are using a base 10 number system when representing the problem in base 10 notation?

Because base 10 is the norm.

Note that in the above statement, 8 does not appear and 2 appears in the same context as 10.

If you disallow the one, you disallow the other, and all solutions are made illegal by the same reasoning.

My problem with your solution is that there are multiple normal answers and you need to distinguish which one. Doing so needs numbers that are not available.

Just as you can assume, when writing the solution that the default notation is implicitly base 10, I can equally assume when performing binary computations to achieve the solution is implicitly provided in 8-bit, 2's-complement notation.

But this isn't so overwhelmingly common as base 10 is.