h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

The easy way to solve my brainteaser is not a mystery. It is a mathematical fact, a method which I used to check the results of my addition, subtraction or multiplication sums when I was at school.

In the present example any combination of digits adding to 18 taken away from any combination of digits adding to 20, will result in an answer where the digits must total 2, 11, 20, or 29.


Examples;-
6275 9236 8345
4383 4545 3627
------ ------ ------
1892 4691 4718

So, it is a very easy solution, as long as you just happen to know a mathematical fact that obviously not many of us know about

It was certainly not covered in my o-level, a-level or degree in maths

I did get the answer, but in an overcomplicated method using MS Excel

It is not something which was taught to me. I experimented with figures, over 70 years ago, and discovered facts which I used
to check for inaccuracies in my calculations.

P.S. Is anyone going to post another brainteaser, or do you want me to post another of the same type of brainteaser?

Then I think that you must have a mathematically exceptional brain.
And for that brain to have been exceptionally active for over 70 years is absolutely fantastic.


Please set another brainteaser - I am ready for more frustration

I'll post one.

These are four codewords in a binary code:

00000000
01010011
11000110
11011000

There are four more codewords in the code. Every codeword differs from every other codeword by exactly 4 bits.

Find the other four codewords...

are they

0000011110
0001001101
0001101010
0001110100

???

sorry - just realised I have a couple of extra leading zero's - not sure what happened there

I reckon that works, groyut!

Your code isn't quite 'balanced' - the first bit in your code is 0 in six out of eight codewords, and the second bit is 1 in six out of eight, but it answers the question I set.

For my answer I had the following codewords:

10010101
10001011
00011110
01001101

I got these by adding combinations of my non-zero codewords (in modulo 2) ie 01010011 + 11000110 = 10010101, etc. I added them in combinations of first + second, first + third, second + third, and first + second + third.


***

Over to you!

Icy

Anyone going to post another?

I've got one written down somwehere - I'll go and dig it out...

Not sure how easy this is to describe (it's easy enough to draw).

Can you draw a system of seven points and seven lines such that:

a) each point lies on exactly three lines
b) each line is drawn through exactly three points

Was it something I said?

I cannot show the drawing here but will try to explain it.

Draw a triangle A B C
Join point A with the middle of line B C.
Similarly B with A C and C with A B
Then a circle to join the new points.

That's perfect!

It's actually a mathematical figure known as a 2-dimensional finite projective plane, or Fano plane. Here's a link:

http://mathworld.wolfram.com/FanoPlane.html

Over to you!

?
56
38
44
44 46 44 44

+ + + +

Is anyone ready to set another brainteaser?

OK...

What last happened 48 years ago, and won't happen again for another 4000 years?

I haven't checked but: the date 48 years ago was 1961 which when turned through 180 degrees reads... 1961! In 4000 years the date will be 6009 which, turned through 180 degrees..........