Fourth in a sequence...

[The Highlander]

Here's a quite interesting (I thought) little puzzle...

What should be on the fourth card?

​

Be sure to post your explanation (in a spoiler?) of how you arrived at what you propose the fourth card should contain.
(There is a specific sequence that determines its content.)

Please don't reply with the answer if you saw the program that the problem was broadcast on. ​

I couldn't get it in the allotted time (40 seconds) and, even after pausing the recording for a few minutes, I was still stumped! lol. (I was a bit tickled when I eventually saw the answer; hence the post here. )

Anyone got any idea what the solution is?

 

[logistic_guy]

Here's a quite interesting (I thought) little puzzle...

What should be on the fourth card?

View attachment 39052​

Be sure to post your explanation (in a spoiler?) of how you arrived at what you propose the fourth card should contain.
(There is a specific sequence that determines its content.)

Please don't reply with the answer if you saw the program that the problem was broadcast on. ​

I couldn't get it in the allotted time (40 seconds) and, even after pausing the recording for a few minutes, I was still stumped! lol. (I was a bit tickled when I eventually saw the answer; hence the post here. )

Anyone got any idea what the solution is?

Spoiler

If no calculations are involved, I think that the pattern:
$\displaystyle 1\times 51$
$\displaystyle 3\times 18$
$\displaystyle 3\times 19$

If calculations are involved, I think that it would make sense to choose this pattern:

$\displaystyle 1\times 52$
$\displaystyle 3\times 18$
$\displaystyle 3\times 19$

Why?

We start with $\displaystyle 3\times 12 = 36$
then
$\displaystyle 2\times 19 = 38$

It looks like increase $\displaystyle 2$ one time, then increase $\displaystyle 1$ two times, then again $\displaystyle 2$ one time, then $\displaystyle 3$ two times, then again $\displaystyle 2$ one time and the patterns continue like this.

$\displaystyle 36 \ \ 40 \ \ 48 \ \ 52$
$\displaystyle 38 \ \ 42 \ \ 50 \ \ 54$
$\displaystyle 39 \ \ 45 \ \ 51 \ \ 57$

where I chose $\displaystyle 52 = 1\times 52$

 

[The Highlander]

Spoiler

If no calculations are involved, I think that the pattern:
$\displaystyle 1\times 51$
$\displaystyle 3\times 18$
$\displaystyle 3\times 19$

If calculations are involved, I think that it would make sense to choose this pattern:

$\displaystyle 1\times 52$
$\displaystyle 3\times 18$
$\displaystyle 3\times 19$

Why?

We start with $\displaystyle 3\times 12 = 36$
then
$\displaystyle 2\times 19 = 38$

It looks like increase $\displaystyle 2$ one time, then increase $\displaystyle 1$ two times, then again $\displaystyle 2$ one time, then $\displaystyle 3$ two times, then again $\displaystyle 2$ one time and the patterns continue like this.

$\displaystyle 36 \ \ 40 \ \ 48 \ \ 52$
$\displaystyle 38 \ \ 42 \ \ 50 \ \ 54$
$\displaystyle 39 \ \ 45 \ \ 51 \ \ 57$

where I chose $\displaystyle 52 = 1\times 52$

Nope!

Both your suggestions are miles off! lol.

You'll have to think again (more laterally this time ).

 

[logistic_guy]

Both your suggestions are miles off! lol.

 

[Harry_the_cat]

Hint??

 

[The Highlander]

Hint??

Hmmm

Difficult without giving too much away but wouldn't be polite to refuse a lady.

On the first card, where it shows: "2×19", perhaps think of it as doubling the number rather than multiplying it by two?

Hope that helps.

 

[Harry_the_cat]

Thanks The Highlander, I think it helped. Is there more than one possible answer though?

Here's a solution:

Spoiler

3x19
3x18
1x1
Reason: Winning at a game of 501 Darts - needs to get a total of 112 on last 3 darts (if I've done the maths right!.

 

[Harry_the_cat]

Ok forget that one, here's a better go:

Spoiler

If you have to "double-out" ie get a double on your last throw (I just read the rules!):
3x18
2x19
2x10

 

[Harry_the_cat]

...and forget that too, although that is a justifiable solution.

Here's the answer I think they wanted (especially if you only have 40 sec to answer):

Spoiler

3x18
3x19
3x20
Darts scores in ascending order (I made it harder than it was!)

Nice little puzzle! Thanks for sharing.

 

[The Highlander]

...and forget that too, although that is a justifiable solution.

Here's the answer I think they wanted (especially if you only have 40 sec to answer):

Spoiler

3x18
3x19
3x20
Darts scores in ascending order (I made it harder than it was!)

Nice little puzzle! Thanks for sharing.

Well Done, Ma'am! You're a star.

Spoiler

You didn't specifically say it but I'm sure it's what you were meaning:-
The sequence is the (12) highest scores attainable by throwing a single dart.

​

I'm now worried that perhaps I did give away too much by my use of the word "doubling" but I just couldn't think of any more obscure hint.

Not that that detracts in any way from your clever deduction! (Especially when even the new site owner (@logistic_guy) didn't have a clue how to solve it and he, apparently, knows feckin everything! )

I thought it was quite an interesting (but solvable for once) puzzle too; from a show where the puzzles are fiendishly difficult and only those with encyclopaedic knowledge (in particularly esoteric areas too) and the ability to think extremely laterally ever get the answers within the 40 second limit!

 

[logistic_guy]

I agree that it was a beautiful puzzle

The logistic guy didn't have a clue on how to solve it and he, apparently, knows feckin everything! )
because he was not given any hints

.......and he, apparently, knows feckin everything! And you're very right about this: I apparently know everything but I am master of none.

I was more focused on relating the sequence of the second card to the first card by prime numbers, squares, sums, etc...
(all tricks failed)

If I knew they were dart scores, of course I would not choose 1x52 invalid input

If 1x52 was valid, my sequence would be correct:
1x52
3x18
3x19

Both your suggestions are miles off! lol.

So, it was very wrong to say I was miles off. That confused me and I stopped to continue solving.

If you said, you were almost there, I would probably get the correct answer.


My question to the smart lady: @Harry_the_cat
How did she figure out that it was a dart game?

 

[logistic_guy]

Some of my working process...

 

[Harry_the_cat]

My question to the smart lady: @Harry_the_cat
How did she figure out that it was a dart game?

Well, the hint did help a bit.
I was playing around with factors for a while. Then Roman numerals, but the 50 (L) threw me. I was wondering why it wasn't 2x25 instead of 1x50. And then it just hit me like a dart!
I made it harder for myself at first by trying to get a total of 501 (I also learnt that the rules of darts say you have to get a double on your last throw). I then admit that my son, who is much smarter than me, knew the answer must be simpler than that if you are supposed to get it in 40 sec. So the final answer was a joint effort.
Was the puzzle from Only Connect?

 

[logistic_guy]

Well, the hint did help a bit.
I was playing around with factors for a while. Then Roman numerals, but the 50 (L) threw me. I was wondering why it wasn't 2x25 instead of 1x50. And then it just hit me like a dart!
I made it harder for myself at first by trying to get a total of 501 (I also learnt that the rules of darts say you have to get a double on your last throw). I then admit that my son, who is much smarter than me, knew the answer must be simpler than that if you are supposed to get it in 40 sec. So the final answer was a joint effort.
Was the puzzle from Only Connect?

Whatever method you used to find the answer, you're still smart.

The last time I watched a dart game was last year, and I never thought those numbers could belong to that game! I was just unlucky to miss that hint.

Was the puzzle from Only Connect?

I don't knowI don't watch puzzle shows!

 

[The Highlander]

Well, the hint did help a bit.
I was playing around with factors for a while. Then Roman numerals, but the 50 (L) threw me. I was wondering why it wasn't 2x25 instead of 1x50. And then it just hit me like a dart!
I made it harder for myself at first by trying to get a total of 501 (I also learnt that the rules of darts say you have to get a double on your last throw). I then admit that my son, who is much smarter than me, knew the answer must be simpler than that if you are supposed to get it in 40 sec. So the final answer was a joint effort.
Was the puzzle from Only Connect?

Yes, indeed, Series 20, Episode 22, as shown here...

 

[The Highlander]

Yes, indeed, Series 20, Episode 22, as shown here...

Ignore the link in the previous post; the video can now be found here....

I'm afraid I uploaded the video to Jumpshare (a free video sharing website) but I didn't didn't bother to create an account there and it would appear that such uploads don't last very long.

I have now registered a Basic (free) account so, hopefully, the link to the video will now remain active indefinitely.