I bought myself an attack worm. Waste of money, it was spineless.
These numbers have the property that if you double them you get a perfect square
2, 8, 18, 32, 50, 72, 98, ...
And these have the property that if you multiply them by 3 you get a perfect cube
9, 72, 243, 576, 1125, ...
Some numbers are in both lists; the smallest is 72 and
2 x 72 = 122, 3 x 72 = 63.
It's not possible to extend this and find a number n such that 2n is a square, 3n a cube and 4n a fourth power. However it was asked on Quora what the smallest number is such that n such that 2n is a square, 3n a cube and 5n a fifth power. Alon Amit showed the answer is 215320524. In full this is
I decided to extend this to the next prime number, 7, and found the smallest n such that 2n is a square, 3n a cube, 5n a fifth power and 7n a seventh power is 21053140584790. This impressive number evaluates to
which has 234 digits.
I think we can continue and add 11, 13 etc. but at this point I ran out of steam!
One of the planes a friend crewed in times gone by has been taken out of service and will be recycled but people who worked on her in the early days were offered a piece of the plane as a memento. My friend chose a window and brought it to the pub where it attracted great interest.
Here is the plane it came from. It was window 6 on the left hand side.
First Flight - 21/01/2005
Type - Airbus A319-111
Serial Number - 2385
Engines - x2 CFM56-5B5/P
Total Hours - 44,668 (21.09.21)
What colour makes you bunged-up? Gold.
What colour lets you into the car? Khaki.
Our garden has a brick planeter, a bit like a wishing well with no well. It was overgrown when we moved here and we never did anything with it until about four years back, when we planted some lavender and a tine holly tree.
Neither exactly thrived, so we decided to redevelop the site. Lavender and holly have been replanted, we hope in a better spot, and we've put in new plants, fewer, but with a more consious design.
The central plant is a quince.This one is ornamental (I think people call these Japonica) but edible quices are a fruit related to apple and pears, and once eaten widely in this country; now unusual and hard to obtain here, although still common in some othe European countries. If you'd like a recipe for baked quince, just ask in the comments.
Let me introduce you. Sal, Amanda.
Why can Dalmatian dogs never hide? Because they’re always spotted!
My donkey ran away on Monday, Tuesday and Wednesday. I thought, that’s three days on the trot.
Given all three labels are wrong, there are only two possible combinations.
1) Label A & P - contents A Label A - contents P Label P - contents A & P
2) Label A & P - contents P Label A - contents A & P Label P - contents A
If we take a fruit from A & P as we are permitted inspecting it will tell which of 1) and 2) is correct.
I wanted to join the snooker club. But there was a queue,
My friend has a thing about barbershops. As soon as he gets in one he's really rude and quickly becomes downright abusive. As a consequence he's gradually been barred from one barber's after another, leaving fewer and fewer for him within reasonable travelling distance.
Eventually it came down to just one. When he went there and asked if they would cut his hair, his reputation must have preceded him. The manager came out and said "We can cut your, but only on condition you treat all our staff with courtesy. Any impolite remark and you're out, and no barber within a fifty mile radius will ever trim your hair again. This is the last chance salon."
Shakespeare used to come to my local. But he was barred.
As Mother always used to say, don’t eat with your mouthful.
Floating in the pond
Fallen plum blossoms
And the moon
Have I told you this before?
It was a joke about time travel.
But you didn't laugh.
I went to the Doctor, I said, I keep imagining I’m biscuits people have with cheese. He said, you’re crackers.
Here is a classic puzzle. I don't know its origin for sure, but I think Martin Gardiner might have published it in his long-standing Scientific American column.
I have three bags and I know one contains apples, one contains pears, and the third both apples and pears.
Each bag is labelled to say what its contents are but unfortunately the labels have got swapped round so all three are wrong.
I am allowed to choose one bag and take out a single fruit. I want to work out what the correct labelling of all the bags should be. How can I do it?
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