In common, you said?
A: 65 92 74 14 56 29
B: 15 22 61 27 82 72
What do the numbers in A have in common that is not shared by the numbers in B.
If that was too easy, try this one:
A: 89 41 56 65 24 84
B: 39 94 46 35 74 11
Problem source: Pradeep Mutalik in Tierney Lab, New York Times.
October 28th, 2009 at 2:39 am
They are in list A.
October 28th, 2009 at 8:40 am
I normally don’t comment on the correctness of suggested answers, but this time I will make an exception.
October 28th, 2009 at 11:23 am
In the first set,
= A mod 3 = 2.
= That is, if you divide any of the first five numbers by three, the remainder will be two.
In the second set,
= A mod 4 < 2.
= A (bitwise AND) 0×02 = 0.
= If you express those numbers in binary, the digit in the 10s spot will be 0.
= int (A/2) = 2 * int (A/4)
October 28th, 2009 at 2:56 pm
OK, my first message was rather frivolous, but there was a serious point behind it. In my experience, it takes no more than a few moments to look casually at a puzzle and have a pretty good idea of how hard and how enjoyable it will be to try to solve it. If it looks too hard, or as if it involves something I don’t much care for, I can just leave it alone and get on with something else. If I do try to solve it, I have a pretty good idea while working on it of how much time and effort there is still to do. It is rare that I embark on one of your puzzles, Jan, and find in it a nut so tough I can’t crack it. I thought that had happened with a puzzle a few weeks ago involving algebra: it looked as though the puzzle entailed solving a quartic. That would have been beyond my powers. Fortunately, however, I’d made a mistake, and, once I’d corrected it, it resolved into a quadratic and the problem turned out to be solvable after all.
By contrast, “Which is the odd one out” puzzles don’t give you that. “What is the next in this sequence?” puzzles are much the same. They give only a small clue as to what branch of maths might be involved, e.g. in this case it must involve numbers. Thus you must look far and wide for a pattern. This makes the effort in looking for a pattern much greater than the difficulty of the pattern warrants, unless the solver is lucky to light on the correct idea early on. There is no clue as to how difficult the pattern is. There is no way to solve the puzzle step by step: you try something, and either it works and you have the answer, or it doesn’t and you are no further forward.