At first sight, all you notice about this numerical series is:
- that they get smaller, then larger, then smaller again.
In this case, it is probably easier not to begin with the first two numbers in the series, but with the 1,
the third number in the series.
What arithmetical operation can be used to derive 1 from 32? Two simple possibilities are:
-31 and /32. It is best to make a note of both possibilities.
What arithmetical operation can be used to arrive at 16 from 1? Here, two simple possibilities are + 15
und x16.
Before you look at the third pair of numbers, you should decide which arithmetical operation is more likely
to be part of the rule governing this series. How can 31 / 32 be related to 15 / 16? The simplest
relationship is between 32 and 16 (32 / 2 = 16). The probability that "/32" and "x16"
are part of the rule is greater than the probability that "-31" and "+15" are part of
it.
Check another pair of numbers against this assumption. Choose a pair of numbers with which you can recognize
a probable arithmetical operation as quickly as possible. In this case, the pair could be 128 and 32. What
arithmetical operation can be used to arrive at 32 from 128? A simple possibility is /4 (which is more
likely to be related to your hypotheses /32 and x16 than the possibility -96).
Now it has undoubtedly become simpler to check the previous pair of numbers. What arithmetical operation
can be used to derive 128 from 16? A simple possibility is x8 (and looks more closely related to your
hypotheses than +112).
In the meantime, you have the following hypotheses:
___, /32, x16, x8, /4, ___
You see that each number is half of the previous number. The first arithmetical operation, which you
don’t know yet, could therefore contain a 64. Take a look at the first pair of numbers. You arrive at
32 from 2048 when you use the arithmetical operation "/64." If you still have plenty of time,
check this calculation. If you are running out of working time, a rough estimation will suffice.
Now you see that, in the rule, two divisions are followed by two multiplications and then another
division. A systematic rule would result if the last arithmetical operation were also a division. The
number used in the final arithmetical operation should be half the previous, that is: 2.
Now apply the rule to the last number in the series: 32 / 2 = 16
The solution to this problem is 16. On the answer sheet, you would have to mark the 1 and the 6.
