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

@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

@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

@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

@kewpie said
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

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

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

What equals 10923?

A further clue: Z=25

KJX ?

@venda said
KJX ?