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

Fascinating!

Now, do I get a sweetie for getting the right answer the hard way?

It's an interesting proof, too, involving remainder theory.

If your number was, say, 654321 and you subtracted 142635 from it, then you can rewrite this as (600000-600) + (50000-5) + (4000-40000) + (300-30) + (20-2000) + (1-100000) Each of these elements is divisible by 9, and so therefore is their sum.

So why are each of these separate elements divisible by 9? It's because they are all multiples of an expression 10^n-10^m [where m and n are integers]

Now both 10^n and 10^m are of the form 9j + 1 [where j is an integer]

So 10^n-10^m is of the form (9j + 1) - (9k + 1) [j,k are integers]

Which reduces to 9(j-k), which has to be divisible by 9.

There, some elementary number theory to amaze your kids with at the weekend.

You get a medal, and a and . but you could now get the answer to any similar teaser in about 2 seconds.
Sorry for delay in my postings, but I am a very slow typist.
I await the next brainteaser.

See,another has been posted while I was typing my last post.

I'm RE's surrogate brainteaser-setter these days, so have a go at this:

Which word comes next in this list? (I'll accept any of three possible answers)

bugles, unrest, grotto, letter, esteem, ?

BUGLES
UNREST
GROTTO
LETTER
ESTEEM
STORMS

Anyone may post another. I do not have one ready and have to go out.

O.K. Here is another brainteaser.

You will be pleased to know that I do not need to know a number.

P-U-Z-T-N
A-G-M-B-G
P-C-B-J-?

Which letter replaces the question mark?

B?

To get this moving, here is another.

A B C D minus E F G H = 4 K 4 5

What is the value of the letter K.

Clues:- A+B+C+D=20 and E+F+G+H=18

A B C D minus E F G H = 4 K 4 5

What is the value of the letter K.

Clues:- A+B+C+D=20 and E+F+G+H=18


All the clues are there. You do not need to know the value of all the letters in order to arrive at the answer. I only need to know the value of the letter K. It should only take less than half a minute to arrive at the answer.

Try different values of the letters ABCD and EFGH, as long as A+B+C+D adds up to 20, and E+F+G+H adds up to 18. When you get the answers see if you notice anything about the results.

Another clue needed?

Just making a pit stop. Looks like the answer is lucky seven.

Yes, you are correct. Did you arrive at the answer the easy way? Do you agree that the answer can be arrived in less than half a minute?

Well done, Czar Dene, for keeping this thread alive . I think the reason that there are so few participants is due to the fact that many of your posers are considered to be too simple for the brighter sparks who inhabit this place.

I'm not sure what 'simple' solution you have in mind for the current teaser - it took me at least two minutes to find the answer:

It can be seen at a glance that by taking 18 from ABCD, with a remainder of 4K45, the value of D must be 3, and the value of C must be 6. Now, since ABCD = 20, and C + D = 9, then A + B = 11. The only possible values for A & B are 4 & 7. Going back to ABCD minus 18, A - 0 = 4, so A must equal 4, and B must equal 7. 7 - 0 = K, so K must equal 7.

Not your 'simple' solution, I'm sure, but sometimes it's quicker to take the low road.

My sum was:-
8264
3519
----
4745
----
There may be several combinations of figures which can give the result 4745.

"I think the reason that there are so few participants is due to the fact that many of your posers are considered to be too simple for the brighter sparks who inhabit this place."

Not so. Your answer was.
4763
0018
----
4745
----
Both E and F could not be zero.

The purpose of the brainteaser was to discover a simple way to solve it in only a few seconds.

However, does anyone wish to post another brainteaser?

"The purpose of the brainteaser was to discover a simple way to solve it in only a few seconds."

That may have been your intention, Czar Dene, but it wasn't stated in posting 2952, which asked simply for the value of K.

I returned from the first stage of my holiday, at least 10 days after that posting, to find that no one had supplied an answer (just as no one had responded or queried my solution to Posting 2949, your previous 'teaser') and that you had added Posting 2953, which stated that it was unnecessary to know the value of all the letters.

After I supplied the correct value for K, you posted to my PS an explanation of the 'simple method' which I find totally incomprehensible.

Perhaps you can link us *on this thread* to a web page with a full explication of this interesting phenomenon?