Construct a
triangle of numbers as follows:
Row 1 contains
two 1's
To construct the
next row write down the previous row. Now find all the pairs
of neighbouring numbers whose sum gives the row number that
you are constructing. Write this sum inbetween each pair.
You have now completed the next row.
For example to
construct Row 2: write down the two 1's from Row 1. The two
1's add to the row number 2 and so 2 is placed between them.
Here is a diagram showing the first six rows:
Now count the
number of numbers in each row. This is a familiar sequence
... it's the prime numbers. Is it always the case that each
row contains a Prime Number of numbers? Construct the next
few rows of the triangle and be amazed.
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No
58
