GCHQ Christmas quiz

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I will need a pen and paper sort of lost track - did work one out but the others need notes
 

PaulSB

Squire
I found #3 very quickly. I've also found an answer to #1, again very quickly, in fact so quickly I can't believe it's correct. Solved #7.
 
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Beebo

Firm and Fruity
Location
Hexleybeef
yes its best printed out and pondered with a pencil

This reminds me of the constipated mathematician who worked it out with a pencil.
 

icowden

Guru
Location
Surrey
Finally cracked it. Number two was a bit devious IMHO and number 5 I had to reverse engineer
I just looked for a 7 letter anagram in the 10 letters and then checked the maths !
I'm sure that there is an additional puzzle in the picture but I haven't figured it out yet.
 
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