Brain Teaser No 1

Squambling

Now, I can't find this word in my dictionary, and Mrs Don is convinced she has seen it in one of the "Harry Potter" books....but which one - she hasn't a clue....

So let me define "squambling" for you....

I believe it is derived from a mixture of "scrambling" and "squaring" a number

To "squamble a number" you take the first (leading) digit, and square it; the second digit is cubed; the third digit is raised to the power of four; and so on. All the derived values are then added together to form a new number - ready for the squambling to begin again.

For example;
18 ----> 1^2 + 8^3 = 513
513 ---> 5^2 + 1^3 + 3^4 = 107
104 ---> 2402......

If you take my friend's age and squamble it, you get a three digit number
If you take that three digit number and squamble it, you get his age next birthday.

How old is my friend at his next birthday?

Cheers

Don

Don,

Your friend will be 47 on his next birthday.

Minky,

Looks like you win that one.

Well done.

Cheers

Don

Blinken heck. A week ago this thread was a vibrant community of like-minded brainiacs. Was it somefink I said ?

Minky,

My guess is that we're all trying to grapple with the astounding fact the answer was 47 and not 42.

cheers,

Dan

Was it somefink I said

most definitely.........

I think you said "47"

so, who's going to explain (in an ammusing and entertaining way) why its 47.....

Cheers

Don

and Dan is going to explain why its 42.....

Cheers

Don

The 4th Dimension

Imagine a 4-dimensional physical space......(hyper-space?)

(this shouldn't be too difficult if you can occasionally imagine imagine yourself transported to Berlin and listening to The BPO and Karajan.....)

What will be the length of a "diagonal" of a "hyper-space" cube of side 10m ?

Cheers

Don

20?

My 'logic'

in 2-d l = sqrt(2) * 10
in 3-d l = sqrt(3) * 10
in 4-d l = sqrt(4) * 10 = 20

cheers

Dan

I think Dan is right.

You create a square from a line by pushing a copy of the line away at right angles and joining the ends that originated together.

You create a cube from a square by pushing a copy of the square away at right angles and joining the matching ends.

A 4D cube is constructed similarly.

In each case one side of the right-angled triangle that can be formed with the diagonal as hypotenuse is the distance you just pushed and the other is the previous diagonal.

So that's enough of a pattern for me.

Paul

Dan, Paul,

Good answers, and reasons

For any "hyper-cuboid" an extended Pythagoras works


Diagonal)= [A^2 + B^2 + C^2 + D^2...]^0.5

Cheers

Don

(Con)-sequences...

.....and the next number in the (picture) sequence is......

Cheers

Don

I can see a very trivial pattern where the next number would be 20, but it's probably loads more complicated that that.

but it's probably loads more complicated that that.

.....errr.....yes and no......

Of course I COULD have just asked for the next number in the series 0, 2, 5, 9, 14.....

But I didn't.

OK the next number IS 20 (and the one after that IS 27....)

But I was hoping for a bit more of an explanation.

Cheers

Don

But I was hoping for a bit more of an explanation.

....like....

How are these numbers related to the shapes?

(=very trivial)

Cheers

Don

But I was hoping for a bit more of an explanation.

.....like.....

if the shape had (say) 20 sides (all internal angles still obtuse) what would be the number?

=very trivial

Cheers

Don

But I was hoping for a bit more of an explanation.

.....like....

if the shape had 100 sides, what would be the number?

=very tedious

Cheers

Don

But I was hoping for a bit more of an explanation.

....like....

is there a neat little formula....

Cheers

Don

= trivial (the formula and me)

Don,
If "N" = number of sides, then number within shape is as follows:-
(N-3) * N/2
or in words (number of sides minus three) multiplied by (number of sides divided by two).
STEVE D

Nicely put, Steve

Cheers

Don

a NOT infuriating puzzle

as Dan M might say "very trivial" and I would agree.

But just to help maintain your sanity whilst loosing the will to live with Jerremy's little puzzle, here is another.....

The grid comprises squares each of area 1 unit.

What is the area of the red triangle?

Cheers

Don

shapes

oh!....nearly forgot.....

the link between the shapes and the numbers 0; 2; 5; 9..... is the number of ...

diagonals


yes I know you knew that, but the others didn't.....

Cheers

Don

Don,

Oddly enough, just a few minutes ago I was reading a book on photography that was talking about 'negative spaces'. Since the area of a triangle is 1/2 * base * height, the area of the red triangle is --

7*5 - 0.5*(3*7+2*3+4*5) = 35 - 47/2 = 11.5

cheers,

Dan

Agreed with Dan!
Steve D