This weeks puzzle

@blood-on-the-tracks said
Unless I am missing some wordplay here, there are any number of solutions
I assumed your lounge was a rectangle, a x b

My lounge is rectangular (should have said that) and there is a unique integer solution.

Incidentally my lounge is p x q. ( 😉 )

@wolfgang59

Then it has to be 6 x 3. All other combinations of a,b give either one as a non integer or the 'square' solution 4 x 4

@blood-on-the-tracks said
@wolfgang59

Then it has to be 6 x 3. All other combinations of a,b give either one as a non integer or the 'square' solution 4 x 4

Yes .... but how to prove it is a unique solution?

@wolfgang59

I would try to explain my logic thus....

Shown on previous page, that if a rectangle is a x b, then for the numerical size of area and perimeter to be equal, b = 2a/(a-2)

Divide out the RHS, we get b = 2 + 4/(a-2)

You have imposed the condition that a AND b must both be integers. Let a take any integer value. Can we discern when b is also integer?

The '2' is irrelevant, as clearly always an integer. Concentrate on the 4/(a -2)

If a is 7 or more, this is a proper fraction, always less than 1 (it simply gets smaller and smaller as a increases). It will never give an integer when added to 2.

So we need to look at a = 1 to 6 inclusive

If a = 1, b= -2 (impossible rectangle)

If a = 2, bottom line = 0, cannot divide by zero, impossible

If a = 3, b = 6 (tick)

If a = 4, b = 4, a solution, but a square

If a = 5, b = 10/3, not integer

If a = 6, b = 3 (a repeat of the only viable solution). qed

@blood-on-the-tracks said
If a = 6, b = 3 (a repeat of the only viable solution). qed

Excellent sir!

A challenge for you
D=3
E=4
ED = 107
DE = 82

What equals 10923?


And finally;
If I have a circular piece of dough of radius Z and depth A, what is its volume when it comes out the oven?

@wolfgang59

I shall take the 2nd for now, it will be a pizza ....v good!

I may get into the 1st later in the week!

I haven't managed to solve Wolfgangs number puzzle but the one in the paper this week is far simpler(not tried it yet)
Insert symbols + - * / into the following string of digits to total 700.
Each symbol may be used more than once, or not at all.
2626262

Welll that was ridiculously easy!!
It only took me 1 attempt!!

@venda said
I haven't managed to solve Wolfgangs number puzzle but the one in the paper this week is far simpler(not tried it yet)
Insert symbols + - * / into the following string of digits to total 700.
Each symbol may be used more than once, or not at all.
2626262

Even I could get it, and I can't do these things:
26x26 +26-2

@kewpie said
Even I could get it, and I can't do these things:
26x26 +26-2

Yes. I think the compiler must be running out of idea's.
Well done anyway.

@kewpie said
Even I could get it, and I can't do these things:
26x26 +26-2

It's good to know your 26 times table!

@wolfgang59 said
It's good to know your 26 times table!

Was a clue to my puzzle;
D=3
E=4
ED = 107
DE = 82

What equals 10923?

A further clue: Z=25

@wolfgang59 said
Was a clue to my puzzle;
D=3
E=4
ED = 107
DE = 82

What equals 10923?

A further clue: Z=25

Ok thanks .
I'll carry on thinking.
is Mr tracks still thinking on it?

KJX ?

@venda said
KJX ?

OBG?

So we have the Problem that the row starts with A=0 going to z=25
AA is 26 AAA is 726 (26 times AA)

If we distrubute the 1093 in the 26 System we get 33*726+1*26+7 So we have the 33rd letter (O) one run of the Alphabet (B) and the 8th letter of the Alphabet since A=0