“I have three boxes, each with two compartments. One has two gold bars One has two silver bars One has one gold bar and one silver bar” You choose a box at random, then open a compartment at random. If that bar is gold, what is the probability that the other bar in the box […]

A problem about motorcycle tyres, related to Time-and-Work or rate-of-work methods. This is not a homework question, nor, as far as I know, a contest question. It is intended as a challenge for Year 10/11 or 15/16-year olds, but should require no knowledge of calculus. Readers will no doubt be familiar with the type of […]

How do you determine what value takes on $a_{0}$ or $a_{1}$ in order to use either the infinite sum formula or $a_{n}$ formula? For example, consider the following two problems: A certain culture initially contains 10,000 bacteria and increases by 20% every hour. (a) Find a formula for the number N(t) of bacteria present after […]

This put in the context of a age problem will be: the product of my age seven years ago and seven years later is some perfect square Since this is a age problem that perfect square has to be between 1 and 100. I’ve try every factor of number between 1 and 100 inclusive, and […]

In a book of word problems by V.I Arnold, the following appears: The hypotenuse of a right-angled triangle (in a standard American examination) is 10 inches, the altitude dropped onto it is 6 inches. Find the area of the triangle. American school students had been coping successfully with this problem for over a decade. But […]

At 10:30 am car $A$ starts from point $A$ towards point $B$ at the speed of $65$ km/hr, at the same time another car left from point $B$ towards point $A$ at the speed of $70$ km/hr, the total distance between two points is $810$ km, at what time does these two cars meet ? […]

I am teaching an elementary student. He has a homework as follows. There are 16 students who use either bicycles or tricycles. The total number of wheels is 38. Find the number of students using bicycles. I have 3 solutions as follows. Using a single variable. Let $x$ be the number of students in question. […]

To be honest, I have no idea how to even start this problem. I’m sorry I don’t have any work to show, but I’m just at a blank. Help? Chapter 2: Problem 27: University B, once boasted $17$ tenured professors of mathematics. Tradition prescribed that at their weekly luncheon meeting, faithfully attended by all $17$, […]

Dr Math told his family to write 4 different integers from 1 to 9 on to the 4 ]

Intereting Posts

Prove by induction Fibonacci equality
How to do a change of variable in an ODE
Optimize $\begin{align} \min _{ (x_1,..,x_n) }\sum_{i=1}^n \sum_{k=1}^n e^{-\frac{(x_i-x_k)^2}{2}} \end{align}$ such that $|x_i|\le a$
Prime Harmonic Series $\sum\limits_{p\in\mathbb P}\frac1p$
Does this integral have a closed form: $\int_0^1 \frac{x^{\beta-1}}{1-x}\log\frac{1-y x^\delta}{1-y}\mathrm dx$?
An example of a derivation at a point on a $C^k$-manifold which is not a tangent vector
A theorem about Cesàro mean, related to Stolz-Cesàro theorem
Prove that $G \cong\mathrm{Inn}(G)$ if and only if $Z(G)$ is trivial
If an integer $n$ is such that $7n$ is the form $a^2 + 3b^2$, prove that $n$ is also of that form.
Analytic continuation of a power series 2
How can I prove formally that the projective plane is a Hausdorff space?
What use is the Yoneda lemma?
Error-correcting codes used in real life
Is an integer a sum of two rational squares iff it is a sum of two integer squares?
Egyptian fraction series for $\frac{99}{70}-\sqrt{2}$