Friday Puzzler II -- another sequence

Re: Friday Puzzler II -- another sequence

Larry Barrett

Most obvious is 8.

Replies

Alex Y

1.2.4.8 obeys the rule

Re: Replies

Larry Barrett

So I would say that the sequence is 2^n, where n=0,1,2,3,...

Sorry, no

Alex Y

Don't think of it as a sequence that can be defined by a few examples, but rather a rule that can be sussed out by finding out what numbers, in combination with the three shown, obey the rule.

2^n certainly works (and would be the "best" solution for a traditional sequence). But you haven't ruled out countless other possible rules, such as

Fibonacci numbers, rounded to the next higher power of 2

Digits that, when combined with the preceding digit form a multiple of 12.

Each number must take as many or more letters to spell as its predecessor.

ad infinitum.

The twenty questions is to figure out which of the "ad infinitum" i am thinking of.

Re: Friday Puzzler II -- another sequence

Larry Barrett

So we there could be many 'fourth numbers' in this sequence. Another example of your unstated rule might be 'all numbers greater than 1 that are divisible by 2'. If I thought that was the rule I should enter 6, 8, 10, ...

Re: Friday Puzzler II -- another sequence

Henry Higginbotham

Are to assume that this sequence isn't hindered by the hint Alex gave for the earlier sequence, that Excel would be no help?

Re: Friday Puzzler II -- another sequence

Alex Y

Actually, the opposite--it would be trivial for excel to be able to give a T/F response to any proposed fourth number, or to any sequence of four numbers.

Re: Friday Puzzler II -- another sequence

Alex Y

Yes, that is an example of a possible rule, and 6 and 10 would also comply with the rule as fourth numbers.

So you get the idea that this rule is not restrictive, in the sense of defining a sequence. It is only a way of assigning T/F to a sequence based on its compliance with the rule.

Re: Friday Puzzler II -- another sequence

Larry Barrett

So how about 3, 5, 7, ...?

Re: Friday Puzzler II -- another sequence

Alex Y

3 does not obey the rule.

5 and 7 do.

Re: Replies

Alex Y

So far, the trials for the fourth number have been 8, 6, 10, 3, 5, and 7.

When put as the fourth number following 1, 2, 4 each of these except 3 follows the rule.

Six potential fourth numbers evaluated so far...

Seems like a good time to guess . . .

Henry Higginbotham

42

Re: Seems like a good time to guess . . .

Alex Y

1,2,4,42 complies with the rule.

Re: Friday Puzzler II -- another sequence

Stuart Hough

If one squares each number, then 16 should also follow the rule.

( A bit late I know, but I just saw this tonight)

Re: Friday Puzzler II -- another sequence

Alex Y

1,2,4,16 obeys the rule, but it is not the squares rule you mention (which doesn't work too well going from 1 to 2 either ;-) )

Some thoughts on this one

Alex Y

Remember that we are looking for the rule here, NOT the fourth number. putting forth candidates for the fourth number is a way of investigating what that rule may be.

In fact, it might be helpful not to think of the goal as a rule. Maybe "descriptor" would be a better word. As we have seen from the examples, the descriptor in question does not define a single sequence.

Let's open up the "20-questions" to include candidate sequences as well as candidates for the fourth number in the given sequence. Larry has already alluded to two (which also fit the descriptor).

So now we have:

YES:

1,2,4,8

1,2,4,6

1,2,4,10

1,2,4,16

1,2,4,42

6,8,10

3,5,7

NO:

1,2,4,3

Re: Some thoughts on this one

Ed in Leaside

Could it be as simple as: the next # must be >than?

It could indeed!

Alex Y

What I find interesting in this is that we have something akin to confirmation bias in solving it. We all start off where Larry did, trying to confirm the pattern that we see in the first three. We then try to find other things that work, and speculate about why they work. But we (or I should say "I") tend to ignore looking for the negative. Finding out what doesn't work can often be as powerful as finding out what does. I'm sure that is what led to your guess.