4,8,1
2,5,3
9,7,6
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Absolutely correct Steve.
Another ‘Well done !’
Unusual Links …
We were planning next year’s summer holidays last night.
Mrs D pointed out the the grandchildren had exactly six weeks school holiday next summer.
“Wow !” said the eldest grandson.
“Yes”, said Mrs D, adding “you guys are really lucky these days, we only ever got 5 weeks”
“No, no !” responded the eldest grandson eagerly, “what I really mean is, there is an interesting link between 6 weeks and 10!. We have been doing factorials at school this week and …”
I stopped him in his tracks. “I don’t think grandma is fully up to speed with factorials. However, I think I know what you mean” said I, as I whispered to him the details of the link …" 
Any ideas ?
I’m surprised I’m the first responder Don; I thought I’d be second 
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Well done Steve.
And nicely encoded so as not to spoil the teaser for others
Hi Ravvie,
As you say, you are the second person to respond. No doubt having solved the link.
Well done!
I was quite surprised to realise just how big 10! is !
10 x 9 x 8 x … x 3 x 2 x 1 has often struck me as a rather modest number, I mean 10 x 9 = 90, even if you do 90 x 8 = 720 it has always seemed that since the following 7, 6, 5 etc are getting progressively smaller, the end result wouldn’t amount to anything special !
Back to a pack of playing cards and 52!
Steve, Ravvie,
For the benefit of anyone browsing who hasn’t yet found a link, would either of you like to explain the link between 10! and six weeks ?
If not, I’ll post my explanation later today or tomorrow.
10! = 3,628,800. This is also the number of seconds in 6 weeks.
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BBC Breakfast this morning mentioned the GCHQ Christmas Challenge, which I also found on the BBC website. It’s aimed at secondary school children and requires a decent level of logical and lateral thinking.
There are 7 questions, the answer to each is a word that can follow Christmas. These 7 answers then lead you to a final challenge.
It took me about an hour to solve it all, and is very cleverly done.
I recommended it to all who enjoy this Brain Teasers thread.
It is fair to say that I probably wouldn’t have managed it in my teens!
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It does seem harder than previous years, it seems it needs a more diverse set of skills, so well done for solving it!
I struggled with 3, getting what I think was one set of three. Mrs R found a different set of three. I think this one is general knowledge which isn’t my strong point.
I had enough answers to get the final answer though.
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Complete Focus
The matrix below needs to be completed.
Fill each blank cell with a whole number between 1 and 30 inclusive. Any such number can be used more than once or not at all.
The numbers in the horizontal rows add up to the totals shown in the darker cells on the left. The numbers in the vertical columns add up to the totals along the darker top cells. The totals in the two long diagonals are also shown in the darker cells at the ends of the top row.
Thanks again Don for another year of entertaining teasers.
I found solving this one a lot more straightforward than finding a way to post my solution 
so hopefully someone else will fare better than me.
I was surprised that I didn’t need the diagonal totals to help solve the puzzle; they just acted as additional corroboration that I’d got the correct answers.
Hi Steve,
Many thanks for your kind words, they really are most appreciated.
I enjoy finding and solving these teasers, and if by sharing them others find them entertaining, that’s an additional bonus !
I’ll post the matrix that includes the missing numbers later today.
I agree with you that this one was more or less straightforward - the ‘10’ in the second from bottom row provided the easy start.
I do have another similar teaser that might require a little bit more thinking. I’ll post it later today or tomorrow, after I (or you) post the missing numbers to the first of these ‘Complete Focus’ teasers.
I started from the single missing one in the fourth row. I was a bit lazy in that I only worked out the method, without bothering with the arithmetic!
My solution above, with missing numbers shown now in red.
I suppose I could have simply listed those missing numbers left/right; top/bottom as
30, 21
12, 20
7, 30
17, 28
16, 28
10
12, 11
Merry Xmas one and all
Enjoy !
As before …
Complete Focus
The matrix above needs to be completed.
Fill each blank cell with a whole number between 1 and 30 inclusive. Any such number can be used more than once or not at all.
The numbers in the horizontal rows add up to the totals shown in the darker cells on the left. The numbers in the vertical columns add up to the totals along the darker top cells. The totals in the two long diagonals are also shown in the darker cells at the ends of the top row.
Merry Xmas one and all,
Enjoy !
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Hmm, I thought I had this right, but one number is above 30….
Anyway, Merry Christmas Don and thanks again for the fun puzzles.
Nice try Mike, and thank you for the kind words.
I had a similar problem. Until I remembered that the diagonals are involved …
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