Articles of puzzle

Liquid levels from the base of a right cylindrical drinking glass

Suppose that a right cylindrical drinking glass with radius r, is partially filled with a green liquid. The amount of liquid in the glass is L cubic units.(A) represents the angle between the major axis of the cylinder and the top of the liquid. H1 represents the distance from the base of the glass to […]

Optimization with a Probability

Imagine two points in $ℝ^2$ at $(-1, 0)$ and $(1, 0)$. You would like to walk from one point to the next in the shortest distance possible. However, there is a line segment coming from the origin to a point $(0, S)$ and $(0,-S)$. In this instance, $S$ is a continuous uniform random variable picked […]

The Efficiency of Random Parking Problem

A few days ago in my Calculus BC class we were given a page of 6 challenging end of the year problems. That was a refreshing change from the drudgery we usually do (WebAssign). One of them went like this: There is a street of length 4 on which cars of length 1 wish to […]

Smallest $k$ s.t. $7x+1=9y+2=11z+3=k$, all positive integers

Find the smallest positive integer, which on dividing with 7 gives remainder 1, on dividing with 9 gives (remainder) 2 and that after division by 11 yields 3 as remainder. i.e., find smallest $k \in \mathbb{Z}^+$ such that $$k=7x+1=9y+2=11z+3 \ x,y,z \in \mathbb{Z}^+$$. The answer is 344 which I got by observing each number. First […]

Knuth's Mastermind Algoritm: “The last step”

I have recently programmed a mastermind game and now I need to program an AI that can solve the puzzle. I have read a lot of guides on this algorithm of Donald Knuth which apparently can solve the puzzle in 5 moves. So i have come so far now that: I have created a list […]

Shortest distance between two moving points

So I found this question on the Internet, which turned out more tricky than I thought: ” The position of boat A is given by $x(t)=3-t$ and $y(t)=2t-4$ The position of boat B is $x(t)=4-3t)$ and $y(t)=3-2t)$ respectively. Find the value of $t$ for which the boats are closes to each other. (distances are in […]

Next number in series

What are the basic/advanced strategies used to find the next number in series. I know the simple ones such as addition, multiplication etc. But recently I came into a question that goes on something like 812, 819, 823, 835, 834, 851(Don’t try to solve this, I changed some numbers and there is no sequence). This […]

Puzzle : cable in the field

Here is an interesting puzzle taken from mathproblems.info: There is a straight cable buried under a unit square field. You must dig one or >more ditches to locate the buried cable. Where should you dig to guarantee >finding the cable and to minimize digging? For example you could dig an X shape >for total ditch […]

Problem regarding the fitting cube into sphere

I was solving the following problem Suppose I have a sphere of radius 1 metre. The sphere is colored with red and blue such that it has disconnected regions of red and blue colors. Now I have to make a cube that fits in the sphere such that Each vertex of the cube touches a […]

Can any $n \in \mathbb{N}$ be reached from 1 by doubling and summing digits?

For $n \in \mathbb{N}$, let $f(n) = 2n$ and let $g(n)$ equal the digit sum (in base ten) of $n$. Can any $n \in \mathbb{N}$ be reached from $1$ after a finite series of applications of $f$ and $g$?