Following on from Karl’s smallest square twin problem, find a (I won’t insist on the smallest) cubic twin. i.e I want something that looks like 123123 = 50³ (that example doesn’t work).
As it has rather a lot of digits, I won’t insist on an explicit number.
A “twin number” is a number formed by writing the same number twice, for instance, 88, 2222 or 1596315963 etc.
What is the smallest square twin of an integer?
To help you on your way…. it isn’t 11.
The subject of the experiment, whom we will refer to as “Chris” was privy to all the details of the experiment in advance, and participated willingly.
One Sunday evening, Chris went to sleep at the observation labs. In another part of the lab a fair coin-toss was conducted, yielding a result of heads or tails. Chris [...]
Choose four points on the surface of a sphere. Each point is independently chosen relative to a uniform distribution on the sphere.
What is the probability that the center of the sphere lies inside the tetrahedron whose vertices are at the four points?
The reason this is titled Sphear is that it is a mix of sphere [...]
A, B,C,E,G,K,M,Q,S,W
What do these letters have in common…?
Unacceptable answers include:-
1. They are all in capitals
2. They all appear in the alphabet
3. They are in alphabetical order etc etc
If n is an integer and f(n) is defined for integers. Find f(n) if it satisfies:
(1) f(f(n)) = n
(2) f(f(n+2) + 2) = n
(3) f(0) = 1
A couple of sequences to extend, based on similar principles…
4 – 9 – 49 – 144 – 441 – ??? – ???
4 – 484 – 28224 – 228484 – 8282884 – ???
Feel free to extend the sequence further if you wish…
Al Gibra wants to attend a meeting of the super-exclusive Mathematical Geniuses Club, but he doesn’t know the secret password that would get him past the bouncer, who looks like a really buff Albert Einstein. Al decided to hide behind some bushes and see if he could figure out the secret admission code. A wild-haired [...]
Not wanting to be embarrassed by revealing her age on her birthday, Grandma instead told the grandkids that if they multiplied her age in 5 years by 5, then multiplied her age in 6 years by 6, and added the two totals together, they would get a number that is 12 times her current age. [...]
H5L9U13
Can you figure out what type of gas this is (the italicised numbers are subscripts)?
