@El Loro posted:I haven't seen yesterday's Only Connect yet, I've recorded it.
Did you watch last nights episode El?
? = ? - ?
x
? = ? / ?
=
? = ? + ?
Place all of the numbers one through nine (once each) in this diagram to make all four equations (three horizontal and one vertical) correct.
@El Loro posted:Got the answer but won't post it yet so that others can have a go
Good deal! 
Another one.
? ? ? ? ? - ? ? ? ? = 33333
Arrange the numbers one through nine into the equation above.
@slimfern posted:What about the next one?.....I have an answer ....will let you go first
I haven't had a chance to think about it yet
In the meantime here's a puzzle I invented.
You have 3 ropes and a lighter. Each rope is very uneven, don't look the same and burn at different rates along the ropes, the only thing in common is that they each take exactly 48 minutes to burn through.
Using only the ropes and lighter, measure 42 inches.
@slimfern posted:Ready with an answer
There are 2 answers:
41268 - 7935 =33333
and 41286 - 7953 = 33333.
Quite a tough puzzle . Would take time to solve it by trial and error so I used a bit of logic. It doesn't take long to realise that it can't be done without carrying back 1 on some of the digits. The sum of 1 to 9 is an odd number as is the sum of the 3 5s. So as the use of carry back adds 1 each time there has to be an even number of carry backs so either 2 or 4 carry backs. Carry backs can only arise with top row 2. bottom row 9 or top 1 bottom 8 where no carry back is used on the numbers to the immediate right or top 3 bottom 9, top 2 bottom 8 or top 1 bottom 7 where a carry back is used on the numbers to the immediate right.
One can see that only 7,8 & 9 appear in the bottom row in the above possibilities so that rules out having 4 carry backs so one needs to use 2.
That means that the carry backs have to be one from 3/9, 2/8 or 1/7 then one from 2/9 or 1/8.
The first number in the top row must be 3 or 4.
If it's 3, then the first carry back can be either 2/8 but that rules out all those for the second carry back options
or 1/7 in which case the second carry back has to be 2/9. that leaves 4,5,6 and 8 as the other numbers - although 8 - 5 = 3 6 -4 doesn't = 3.
So that means the top number has to start with 4. Which means that the numbers to it's right are:
3/9 with the next being 1/8 but that leaves 2,5,6 and 7 which doesn't work,
or 2/8 but the options for the next number won't work,
So you are left with the only option which is 1/7, then 2/9 (so 412 top, 79 bottom = 333) and the remaining digits 3,5,6,8 of which 6-3 = 3 and 6-5 = 3 leading to my answers above.
Here's another couple of puzzles.
Without using any calculator, computer etc or writing anything down
A) Add up the numbers 1 to 100
B Prove that there are an infinite number of prime numbers (a prime number is one which is only divisible by 1 and itself, for instance 13).
Both puzzles are simpler than they might seem
Exits thread left @El Loro posted:Here's another couple of puzzles.
Without using any calculator, computer etc or writing anything down
A) Add up the numbers 1 to 100
B Prove that there are an infinite number of prime numbers (a prime number is one which is only divisible by 1 and itself, for instance 13).Both puzzles are simpler than they might seem
A) 5,050 ............many more than brain cells I have left
@El Loro posted:5,050 is correct (1+100=101, 2+99=101, and so on to 50+51=101 so 50 x 101 = 5,050)
Me thinks you have a lot more than 5,050 brain cells left
Certainly doesn't feel like it 
I do know the answer to B...but is not easy to write it down 
Am still working on your own puzzle 
@slimfern posted:Certainly doesn't feel like it
I do know the answer to B...but is not easy to write it down
Am still working on your own puzzle
If you multiply every known prime number (excluding 2), then add 2 or deduct 2, the resulting number cannot be divisible by any of those prime numbers as 2 isn't divisible by any of those numbers. Therefore the resulting number must be an unknown prime number or a multiple of unknown prime numbers. That means there's an infinite number of prime numbers. 
3x5x7x11x13 = 15015
Neither 15013 or 15017 are divisible by 3,5,7,11 or 13 so must be prime numbers or multiples of different prime numbers (they are both prime numbers),
@El Loro posted:If you multiply every known prime number (excluding 2), then add 2 or deduct 2, the resulting number cannot be divisible by any of those prime numbers as 2 isn't divisible by any of those numbers. Therefore the resulting number must be an unknown prime number or a multiple of unknown prime numbers. That means there's an infinite number of prime numbers.
3x5x7x11x13 = 15015
Neither 15013 or 15017 are divisible by 3,5,7,11 or 13 so must be prime numbers or multiples of different prime numbers (they are both prime numbers),
Nicely put El
@El Loro posted:I haven't had a chance to think about it yet
In the meantime here's a puzzle I invented.
You have 3 ropes and a lighter. Each rope is very uneven, don't look the same and burn at different rates along the ropes, the only thing in common is that they each take exactly 48 minutes to burn through.
Using only the ropes and lighter, measure 42 inches.
@slimfern posted:Certainly doesn't feel like it
I do know the answer to B...but is not easy to write it down
Am still working on your own puzzle
Do you want me to say what the answer is? It's a puzzle which may seem hard but once you have the answer it seems simple
@El Loro posted:Do you want me to say what the answer is? It's a puzzle which may seem hard but once you have the answer it seems simple
I wrote it down and left it on the games table for the household to have a go at, but it just got buried under jigsaw pieces 
Put me out of my misery
@slimfern posted:I wrote it down and left it on the games table for the household to have a go at, but it just got buried under jigsaw pieces
Put me out of my misery
Light one rope (A) at both ends and one end of both the other two ropes (B & C).
As a rope takes 48 minutes to burn through, A will have burned through after 24 minutes, and there are 24 minutes left to burn on B & C.
So light the other end of B. After 12 minutes that's burned through and there's 12 minutes left on C.
So light the other end of C and that's burned through after 6 minutes.
24+12+6 = 42 minutes.
My puzzle is a variation on a puzzle where there are two ropes which each take 60 minutes and you have to measure 45 minutes (A takes 30 minutes to burn through, 30 left on B which then burns through after 15 using the same procedure as my puzzle).
@El Loro posted:Light one rope (A) at both ends and one end of both the other two ropes (B & C).
As a rope takes 48 minutes to burn through, A will have burned through after 24 minutes, and there are 24 minutes left to burn on B & C.
So light the other end of B. After 12 minutes that's burned through and there's 12 minutes left on C.
So light the other end of C and that's burned through after 6 minutes.
24+12+6 = 42 minutes.
My puzzle is a variation on a puzzle where there are two ropes which each take 60 minutes and you have to measure 45 minutes (A takes 30 minutes to burn through, 30 left on B which then burns through after 15 using the same procedure as my puzzle).
Easy when explained ....cheers El 
@Former Member posted:23, 45, 14, 68, 86, 41, ?, 32
I've got the answer
The number appears in the title of this old American TV comedy series:
https://www.imdb.com/title/tt0...8/?ref_=nv_sr_srsg_0
@Former Member posted:23, 45, 14, 68, 86, 41, ?, 32
Seems fairly straightforward.
There's a BBC article today about a GCHQ recruit. It starts with this:
What comes next in the sequence? 7, 8, 5, 5, 3, 4, 4 ?
Link to article which has the answer at the end:
https://www.bbc.co.uk/news/newsbeat-59386703
Two possible answers depending on whether we are looking at asequence or just the figures on that page.
40 or 96 - Am I a genius then?
@Extremely Fluffy Fluffy Thing posted:Two possible answers depending on whether we are looking at a sequence or just the figures on that page.
40 or 96 - Am I a genius then?
I agree. Am I a "genious" too
