Math Is Fun Forum

Hey bobbym (:

We must eliminate the apparent chance they are both right or both wrong (25% each for total of 50%). Then:

Sorry, 837. That should be the number of valid solutions with the first digit multiplied only by 1 (I forgot) and the others multiplied by positive integers from 1 to 10. Infinite solutions are for when you extend to any coefficients satisfying post #3's terms. And that's just a small part of the range of answers with very restricted boundaries, within one fixed application of operations (multiplying by coefficients and summing).

Cannot speak for answers with no repetition or reordering and +,*,() only, though.

I concur However, there are infinitely many correct solutions of a similar type.

Hi phrontister (:

Ignore the OP, Your formula:

Satisfies the three conditions of post #3 and is also correct.

I meant to add that it is expected to be solved without repetition of numbers as well.

But regarding the supposed solution with extra conditions - Use the numbers once in their given order to produce the answers using only +, * and () in the same manner - while it might exist and be valid, I would not trouble myself very much over it, since the creator of this problem on a different site seems too mathematically illiterate to understand what we are even doing here.

Hey (:

My answer:

The paramount ambiguity in the paradox is whether the content of box A is, or is not, somehow dependent on the decision. It appears to many not to be because in fact there cannot be a physical causation. Those with this view are content to assert that taking box B as well will yield strictly $1k more than not doing so, irrespective of the prediction. However, the contention here is that this view is in error due to an overlooked inference. While the decision does not cause the content of the box, the prediction does; and the prediction is thoroughly correlated with the decision. Although the decision does not cause the prediction, the prediction (and hence the content of the box) can be inferred from the decision. Therefore, the content does indirectly depend on the decision. Those who intuit that the content of the box is fixed may be answered: Yes, but only in the sense that the decision is fixed; for the one invariably corresponds to the other. (Incidentally, if the expectation of the choices are modelled as functions of the accuracy of the predictor, it is determined that, due to the high stakes, for box A alone to be preferred the predictor need only be more than 50.5% accurate. Box A alone is potentially a winning strategy even with an ordinary human predictor!)

Hi thickhead, hahahah

What OP is looking for is not necessarily a mathematical formula, but any algorithm for manipulating those numbers into those answers. For example, the first line might be

, which works for only the first line because for example

. The only rule is that exactly the same algorithm has to work for all three lines.

When blown up, it is not clear enough to read

Looking at it more algebraically, and dealing with only the method of multiplying each digit by a separate number and summing the products, I determined, using the notation

to denote the number multiplied by the nth digit, that only the set of numbers satisfying the following three conditions will evaluate to the correct answers:
1.

2.

3.

Hey (: