To: HIQ
From: D5B (Jon Ripley)
Subject: Question Answers Pt.2
Here are the answers to the last three
questions...
These questions dealt with adding
together the digits of a number to
make another number, so for the number
1234 you would add 1+2+3+4 to make 10,
and because you still have more than 1
digit you would add 1+0 to make 1, the
final answer.
8. 184 = 1+8+4 = 13 = 1+3 = 4!
9. 98832365 = 9+8+8+3+2+3+6+5 = 44
= 4+4 = 8
10. 4444
This one was a bit more difficult! You
could either take it as a trick
question leaving.
4+4+4+4+4+4+4+4 = 32 = 3+2 = 5
Or you could take it as a literal
number and add all the digits in the
number 4444 to the power of 4444 (ie
4444 multiplied by itself 4444 times!)
I won't give the solution here as it
is over 16,500 digits long, I can
however, tell you that if you add all
those digits together you get 7. In a
future issue I may tell you how to
calculate such large numbers.
More puzzles coming soon!
HIQ is moving across to BBC User Group
if you have any puzzles/questions that
you would like to see in this section
in future issues, you are welcome to
send them in to 8BS, or me at BUG.
To: HIQ
From: D5B (Jon Ripley)
Subject: Question Answers Pt.1
In a previous issue I posed a few
questions for you to think about. Here
are the answers!
The next number in the sequence...
1. 3 4 5 8 1 7 7 10 3 ...
The next number is 6.
2. 5 2 3 3 9 8 6 1 10 ...
The next number is 3.
Congratulations to those of you who
managed to work these out. If you are
still in the dark, they are the first
10 numbers produced by the typing the
following after switching your BBC on.
FOR X=1 TO 10:PRINT RND(10):NEXT
Question 1 is the numbers given using
BASIC 4 on the Master. Basic 2 on
Electrons, BBCs and some B+s gives
the numbers in question 2.
3. 1 3 6 10 15 ...
This is a simple numerical series where
each number in the list is the
position of the number in the list
added to the previous number, thus...
0+1=1, 1+2=3, 3+3=6, 6+4=10, 10+5=15
so the next number is 21 or 15+6.
Next you were asked to find the next 2
numbers in a series.
4. 9 1 8 2 7 3 ...
The next two numbers are 6 and 4, each
pair of two numbers adds up to 10.
Another way of looking at it is as two
superimposed series, one going 9 8 7 6
and the other going 1 2 3 4 etc.
5. 3 1 4 1 5 ...
There are two answers to this one, it
could be 1 then 6 if you see it as a
list of consecutive numbers with a 1
separating them, if so the series
would continue with 1 7 1 8 1 9 1 etc.
The second way of seeing this is as the
digits of PI, which are 3.1415926 etc.
So the next two digits in the sequence
would be 9 then 2.
6. 12 23 34 45 54 43 ...
If you think of this one without
thinking of maths you will notice a
pattern. With 32 and 21 being the next
two numbers.
7. What is 9.11612581436 ?
'A number!' is the first obvious
answer that springs to mind, although
you will technically be correct you
would have answered incorrectly.
This is in-fact another PI related
question. If you take a closer look at
the number you might notice that it
consists of a sequence of square
numbers. (A square number is a number
made by multiplying a number by
itself, so 16 is 4 squared because
4*4=16.)
Splitting this number into separate
squares you will get...
9 1 16 1 25 81 4 36
Taking the root of the squares you get
the numbers:
3 1 4 1 5 9 2 6 which are of course
the digits of PI.
The answers to the last three
questions are in the next message!