Trick of Mind

Here is a puzzle to keep you busy on a cold winter’s night. Perhaps more than one!
The challenge is to express ANY positive integer using the number 2 precisely four times, and using only well-known mathematical symbols. (You can’t make up your own!)
Here are the first four.
1= (2+2) / (2+2)
2= (2+2) + (2+2)
3= (2 x [...]

Merry Christmas all!
Here’s a good one. Tell me which letter(s) this code lead to and how you found out.
8/1P6/1P6/1P1PPP2/1P2P3/4P3/4P3/8
HINT: Forsyth Notation

Chris, a citizen of Karlonia commits a severe crime and is brought to the castle to face his punishment. Karl, King of Karlonia though a ruthless tyrant, is a man of his word. Karl says to Chris “You shall make a statement. If it is true, I will sentence you to 20 years in prison. [...]

I received my set of twelve balls from the pool hall, so that I could test my solution to the twelve ball problem. But when I opened the box I saw to my horror that the manufacturer had included three extra balls! Now I had 15 identical looking balls, only one of which is either [...]

Yesterday I met a zookeeper. I asked him how many birds and beasts he had in his zoo. He told me that there were 30 heads and 100 feet in his zoo. How many birds and beasts does he have, assuming that all birds have two feet and all beasts have 4 feet?

As you may have already noticed, this Christmastide notification is not the average, everyday, run of the mill, ho-hum quality. No! This is re-usable. What you may not have realised yet is that this may well be the last seasonal greeting you will receive from me. That is why it is re-usable.
“Seasons Greetings” can cover [...]

It’s lunch time in the office, and people are getting hungry. Let’s say most people bring their food to work, keep it in the refrigerator, and microwave it around noon. There is a hallway outside the break room that can hold a large amount of people. At 12:00:00 the office employees may take their lunch [...]

Snow starts falling at some time before noon on a cold December morning. At noon a snow plow starts plowing a road (as if!!).
At 1 pm the plow has advanced 2 miles, but it takes another 3 hours to do the next 2 miles.
What time did it start to snow?
And is plow spelt [...]

During WWII, the Royal Air Force called upon a mathematician to improve their bombers. Specifically, they wanted to reduce the chances of them being shot down.
Bombers are relatively slow moving targets escorted by smaller fighters to protect them from air attacks. But antiaircraft fire would occasionally knock them down.
So a reasonable solution was [...]

Is frozen milk heavier than non-frozen milk. This is a trick question, it is posted on ToM. Think carefully before you answer. Please substantiate your Yes or No answer. Could also be a double or triple bluff, but it is the weekend…