# Estimate and guess on the numbers

Smart estimates on the calculation results. If calculation result is an integer, them the simplest guessing technique is using divisors and check the last digit (that is the units-place digit).

There are more involved estimate techniques of expressions. Specifically, radicals can be approximated by fractions, so expressions involved radicals can be approximated.

# Selected problems — Math Kangaroo and scenario of math games

Sample problems from Math Kangaroo / Math Game Scenarios. Have a try on the fun problems!

# Perfect Beauty of math in the Symmetry

A brief discussion about symmetry and asymmetry (Asymmetry means not being symmetric).

In solving geometric problems, the property of symmetry can be a useful clue for some problems — but be aware that there are pitfalls too!

# Adding two fractions with different denominators

A discussion on how to add two fractions with different denominators; with both a clear presentation of concepts and use visualize help.
For educators, when a student has made a mistake in calculation, sometimes we have to understand first why student thinks and does in that way, and then persuade them with clear concepts and strong reasoning.

# Smart scrambling of digits onto pyramid to match edge-endpoint equations

The problem is about filling numbers 1 – 11 into all vertices and edges of a tetrahedron, and the numbers assigned to edges equals the numbers assigned to its two endpoints.

(It’s not really scrambling BUT looks like scrambling until you know or find the equalities on edge-endpoint numbers). The problem is interesting — but you got to know where to look, and how to search for a solution!

# Full Solution to guessing the numbers pair problem

We reformulated the problem in previous post as numbers pair, both perfect squares.

Several approaches to the problem! Each has its own flavor and deserved mentioning.

# Guess the numbers pair: both perfect squares, with a given difference

Given an expression of n, like n square plus 6n plus 24, and declare it’s a perfect number. Can you find the integer n?

Seems clueless, eh?
And what’s the pair of numbers: both perfect squares, as mentioned in the title? Not in the original problem, but it’s one clue calling for you to construct; and to solve!

# Answer to the Mysterious Unbalanced Sheets on Loans

The answer to the Hunchbacked shopkeeper’s story: Simple! Both sheets are indeed balanced.
Read this post for more explanations!

# Mysterious Unbalanced Sheets on Loans – story told by hunchbacked shopkeeper

— It’s a mystery!

Once there was a hunch-backed shopkeeper.

And he told the following story: