Wrong Number in a SequenceDate: 08/13/99 at 15:39:13 From: Samantha Bossingham Subject: Series question I came across this question on a test for management. The question is as follows: In the following sequence, one number is incorrect in the sequence. Which one is wrong, and what number does it need to be replaced with? Can you explain this sequence? 1, 1, 2, 2, 6, 18, 21, 84, 88, ... The choices were: a. 3 b. 4 c. 9 d. 24 e. 48 What is the answer? I tried going through multiplication and division, adding and subtracting... I can't figure it out. Help! Date: 08/21/99 at 01:36:29 From: Doctor Douglas Subject: Re: series question Hi, Samantha. This is a very interesting puzzle. Here's the way I would look at it: In the sequence {1, 1, 2, 2, 6, 18, 21, 84, 88, ...} I would first focus on the bigger numbers, since whatever rule governs the series should be easier to spot there. There are lots of plausible connections between small numbers such as 1 and 2 and 6. To sort it out from all these possibilities seems very difficult. But at the larger numbers, there are fewer plausible relationships. Indeed, that 21 and 84 seem to be connected by the operation (multiply-by-four). And then 84 to 88 seems to be accomplished by the simple operation (add-four). So we could write things like this: 1 1 2 2 6 18 21 84 88 (*4) (+4) Hmmm, now how do we connect 18 and 21? Perhaps the simplest is to say that we need to add 3: 1 1 2 2 6 18 21 84 88 (*3) (+3) (*4) (+4) I've also added the (multiply-by-3) that seems to connect 6 to 18. Now perhaps you can see a pattern developing. Try exploring this and see if it leads anywhere toward helping identify the "wrong" number and what its "correct" value should be. If you find this hint confusing, please don't hesitate to write back. - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/ |
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