I found this last puzzle very interesting. The most intriguing aspect to me was multiplying line seven to get the total. I tried it but it didn't work - until I checked my calculations! By the time you get to the seventh number you have 8 of the first number and 5 of the second. At the sum of all to line 10 you have 88 of the first and 55 of the second, so 11 times the 7th line total = the grand total of all the numbers. Incredible.Paidion wrote:

Now for the really impressive part! Ask your friend to take use the calculator to divide his number in line 10 by his number in line 9. In this case it will be 1995 ÷ 1233. Then ask him to write down the first three digits of his answer. Now have him turn the paper over and look at the other side. He will see the very number he wrote down, that is, 1.61

As soon as I saw that the answer to the question was going to be 1.61 I figured that this was going to be a Fibonacci sequence or the 'Golden ratio', which it is. I never cease to be amazed at how this pattern of numbers shows up in nature, architecture, human anatomy and even ancient religious sites such as Stonehenge.

Graeme