PRIZE PUZZLE FOR APRIL 2007
NUMBERS
The puzzle this month is to identify as many of the following 10
numbers as you can. They are all simple functions using simple
constants with roots, powers, logs and reciprocals. For example,
most people would recognise the number 3.1415926535 as pi whilst
1.772453851 requires some experimentation with a calculator to
discover that it is the square root of pi. All are rounded to the
precision given.
0. 0.14285714286
1. 1.618
2. 3.16227766
3. 0.31831
4. 6.2831853
5. 0.30103
6. 0.69314718
7. 4.6415888
8. 0.43429448
9. 65536
You don't have to answer all 10 but he/she who identifies the
largest number will be the winner.
ANSWERS (scroll down)
Here are the answers:
0. 0.14285714286 =1/7
1. 1.618 =golden ratio = 2/(sqrt(5)1)
2. 3.16227766 =sqrt(10)
3. 0.31831 =1/pi
4. 6.2831853 =2pi
5. 0.30103 =log10(2)
6. 0.69314718 =ln(2)
7. 4.6415888 =cuberoot(100)
8. 0.43429448 =log10(e)
9. 65536 =2^16
I received three entries. They were from John Stafford,
Richard Burkill and Peter Greenhalgh. John Stafford won the draw
for the £5 book token.
Notice that all the numbers are simple functions of simple
constants (except for the Golden Ratio which is very well known).
Here is another supplementary: 1.359140914 which I have given to
9 decimal places to reveal a clue.
