Judging by the response, I guess these puzzles are harder than I anticipated.
Here are some general hints on the puzzles, followed by specific hints on the unsolved problems that you can highlight to read. General hints: The only operations that are used in the problems are the arithmetic operations and squaring. Two of the problems are non-numeric — they rely on the representation of the number in ways other than using Arabic numerals. Specific hints: Highlight the blank space after the problem number to read. Compare the numbers in the In and Out sets that have common second digits.
What do the second digits in the In set have in common? Notice the restricted values of the numbers in the In set. This problem uses a non-Arabic representation. The word lover puzzle solution is that the In group has the vowels in correct alphabetical order, as opposed to the Out group which has the vowels in random order. The rule seems to be that the vowels occur in alphabetical order in the words that are IN, but not in the words that are OUT.
This seems somewhat arbitrary, but the fact that it works for all twelve of the words seems significant. Ironically, all of the IN words relate to outwardness , while all of the OUT words relate to inwardness. There is indeed a venerable tradition of characterizing inductive reasoning as a move from the particular to the general and vice versa for deductive reasoning. But it is worth noticing that this is not the conception of induction generally accepted by logicians, who treat inductive inferences as those that are less than certain.
Similarly, in a good inductive argument the premises should provide some degree of support for the conclusion, where such support means that the truth of the premises indicates with some degree of strength that the conclusion is true.
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Socrates is snub-nosed and Greek. So every Greek is either snub-nosed or not identical to Socrates. Those examples serve to show that deductive arguments as logicians understand them do not move from general premises to a particular conclusion, nor are general-to-particular arguments always deductive. Contemporary logicians, though, would call this a clear case of deductive reasoning. From a formal logic point of view, you are absolutely correct: all deductive conclusions are entailed in the premises, while inductive ones are not. I was using a particular specific instance of inductive reasoning: that of formulating a general rule from particular data that we possess.
This is the way in which scientific theories are born. Revision and extension of existing theories is the way science spirals asymptotically toward absolute correctness, never quite reaching it, or at least, never being certain that it has. In case of these puzzles, however, the inductive rule only has to meet the given data points.
Problem 1: All are congruent to 2 mod 3 —as in, each number, when divided by 3, gives a remainder of 2. My method for problem 1 would be: If the sum of the two digits of each number is 5 or 11, the number belongs to the In set. Otherwise, it is in the Out set. For problem 2 If the sum of the two digits of each number is even, the number belongs to the In set.
Second series was even better, producing eclipse. Am stumped so far by the remaining four. And a note to ascetic, anemic Alexia: spaghetti! Bigger, not smaller! I was going to include a few using three-digit numbers. Good luck! Only the first two and easiest of the groups have yielded up their secrets. But the pairings are arbitrary. What we are looking for is a rule that can unambiguously classify a given number as belonging to the In or Out sets. Average Review. Write a Review.
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