GCHQ Christmas Challenge for Kids

Question 1 says. "These clocks show a four-letter word. Can you work it out."

My initial thought went to the fact that the question is using the clocks to represent a word. I wondered if that was a clue in itself? I thought, are the clocks representing the answer by simply being clocks. I therefore wondered if the four-letter word is, "TIME"

If the answer is TIME, I had to figure out how I might get to that word via the times shown on the four clocks. I may have worked out the answer to Question 1, but kind of did it backwards?:

Clock one = 8pm
Clock two = 9am
Clock three = 1pm
Clock four = 5am

If we turn the four clocks into 24-hour clocks, and use that displayed 'time' (number) to represent letters of the alphabet, does it look like this:

* Clock one, 8pm. 8pm = the 20th hour of a 24-hour clock. The 20th letter in the alphabet = T
* Clock two, 9am. 9am, simply the 9th hour, therefore the 9th letter in the alphabet = I
* Clock three, 1pm. 1pm = the 13th hour of a 24-hour clock. The 13th letter in the alphabet = M
* Clock four = 5am. 5am, simply the 5th hour, therefore the 5th letter in the alphabet = E
TIME


At the top of the card in my post #2, it says, "The seven questions below each have a one-word answer which can follow 'Christmas'. This kind of makes sense to me, Christmas Time.

Who wants to look at question 2?
 

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I'm struggling with question 3, so I moved on to question 4 which reads like this.:

MI x MI = MAA
TI + TI = RA
DO - SO +TI -MI = RE

What is the answer to
RE x RE = ?


Remember the person who set the question says the word answers must follow on from the word Christmas. I think the answer to question 4 is TREE, as in Christmas TREE.

MI x MI = MAA. We have to come up with two same two-digit numbers that when added together give a three-digit number. As I see it, 'MI' can't be greater than 32, as 32 multiplied by 32 = a four-digit number of 1024. So with that in mind, the letters M & I can only be between 1 & 3.

To me it looks like this.

MI x MI = MAA
12 x 12 = 1 4 4
I can't see 'I' as being zero, as it would look like this. 10 x 10 = 100. That would put zeros in the answer of MAA, and I don't see how both 'I' & 'A' can both represent zero?

TI + TI = RA, therefore 'initially' looks like this to me, based on already established that 'M' = 1; 'I' = 2; 'A' = 4:
TI + TI = RA
?2 + ?2 =?4

TI + TI = RA
to me then looks like this. I did wonder if T represented a different number than 3, but other numbers didn't work out when I carried them through the other equations.

32 x 32 =64
Then we have
DO - SO +TI -MR = RE, which looks like this to me based on what we have established so far. The rest of the working out became a process of number elimination.
DO - SO +TI - MI = RE
? ? - ? ? +
32 - 12 = 6?
96 - 23 + 32 - 12 = 60


The final part of the question then.
What is the answer to:
RE x RE = ?
RE x RE = TREE
60 x 60 = 3600

Christmas TREE
 

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