## March 22, 2020

### Challenge Problem 17: Three Runners Puzzle (From India’s Civil Services Exam)

There are three runners X, Y, and Z. Each runs with a different uniform speed in a 1000 meters race.

If X gives Y a start of 50 meters, they will finish the race at the same time.

If X gives Z a start of 69 meters, they will finish the race at the same time.

Suppose Y and Z are in a race. How much of a start should Y give to Z so they would finish the race at the same time?

### Challenge Problem 16: No One Selected The Correct Answer To This Test Question

The product of 3 integers x, y, z is 192. Also z is equal to 4, and p is equal to the average of x and y. what is the minimum possible value of p?

### Challenge Problem 15: An Amazing Result of Complicated Exponent Problem

This puzzle was created by a MindYourDecisions fan in India. What is the value of the following infinite product?

### Challenge Problem 14: Cube Inside Hemisphere Puzzle

A hemisphere has a radius of 10. A cube is constructed so its bottom face has the same center as the hemisphere, and the four corners of its top face just touch the hemisphere. A green line is constructed from the center of the cube’s top face to a corner of its bottom face, as shown. What is the length of the green line in the following figure?

### Challenge Problem 13: What Is The Area of Triangle 1984 AIME?

The American Invitational Mathematics Exam (AIME) is the second qualifying test for selection in the US Mathematical Olympiad team.

### Challenge Problem 12: Tricky Algebra Problem From Nepal Olympiad

Suppose:
ax + by = 5
ax^2 + by^2 = 10
ax^3 + by^3 = 50
ax^4 + by^4 = 130
Calculate the value of:
13(x + y – xy) – 120(a + b)

### Challenge Problem 11: What Is The Area of The Inscribed Triangle In A Rectangle?

In square ABCD, what is the area of triangle BEF?

## March 21, 2020

### Challenge Problem 10: Radius Of Circle Between Quarter-Circles

In a square with a side length of 1, two quarter circles are drawn and a circle is inscribed between the quarter circles, as shown in the diagram. What is the radius of the inscribed circle?

### Challenge Problem 9: Clever Logarithm Problem

Simplify the following product: (log_2 3)(log_3 4)(log_4 5)…(log_127 128)

### Challenge Problem 8: Solve For The Radius, 2017 AMC 12A Problem 16

As shown in the diagram below, circle D is internally tangent to circle A and externally tangent to circles B and C. If circle B has a radius of 2 and C has a radius of 1, what is the radius of circle D?

### Challenge Problem 7: Square Angle Bisector Puzzle – Think Outside Or Inside The Box!

In square ABCD, angle EAD is bisected by AF. If BE = 36, FD = 64, solve for AE.

### Challenge Problem 6: What Is The Side Length of Octagon Cut From Rectangle?

An octagon with equal side lengths is made by cutting the corners from a rectangle that has sides of 4 and 6, as shown below. What is the side length of the octagon?

## March 20, 2020

### Challenge Problem 5: The 8 – 4 = 61 Matchstick Puzzle

Here’s a fun challenge. In the picture below, move only 2 sticks one time to make a correct equation.

### Challenge Problem 4: Four pi’s to represent any number!

This is a fun problem for Pi Day. Write an equation using exactly four π’s that equals 0. Then do the same for 1, 2, 3, and see how many you can solve. For a real challenge, write an expression that can equal any integer n.

## March 19, 2020

### Challenge Problem 3: 2019 IMO Question 1

ℚ is for quotient – which is how rational numbers are identified.
ℤ is for Zahlen – the German word for integers.
– Doctor Paul, The Math Forum

The International Mathematical Olympiad (IMO) is an annual competition for pre-college students. Over 100 countries participate, and each country sends a team of its six most elite competitors.

### Challenge Problem 2: Oxford’s Tricky Triangle Ratio Question

This is from the 2018 Oxford Math Admission exam.

Two triangles with areas s and t are inscribed in a circle, as shown.

### Challenge Problem 1: Solve For The Red Area

Here’s a fun little geometry problem. Each small square has a side length of 1. What is the area of the red shape?

## April 17, 2015

### Trọn Bộ Sách Calculus Chuẩn Mỹ

Yêu Tiếng Anh - Trọn bộ sách toán Calculus chương trình Đại Học Đại Cương của Mỹ. Bộ sách sẽ cho bạn hình dung một cách khái quát cách học và dạy chương trình Toán Đại Học của Mỹ. Nó giúp cho bạn trải nghiệm trước khi tiến vào chương trình học chính thức tại một trong các trường Đại Học của Hoa Kỳ. Bạn nào không có ý định du học ở Hoa Kỳ cũng nên xem đây như tư liệu tham khảo bổ ích cho việc tiếp thu môn Toán bằng Tiếng Anh.

## January 11, 2014

### Từ Điển Toán Học Trong Tiếng Anh (Part 1)

Học Toán bằng Tiếng Anh không thể không có Từ Điển Toán Học. Nhằm giúp các bạn dễ tiếp cận các bài Toán cũng như thuật Toán bằng Tiếng Anh, Tôi giới thiệu đến các bạn một số thuật ngữ Toán bằng Tiếng Anh bên dưới. Hi vọng, một phần nào đó không những giúp cho các bạn tìm hiểu các thuật Toán bằng Tiếng Anh một cách dễ dàng, mà còn tạo tiền đề cho việc học Toán bằng Tiếng Anh sau này của các bạn được tốt hơn. Học đi đôi với hành, click vào đây để xem những bài liên quan nhé. Xem mục luyện thi đại học tại đây.

## September 4, 2013

### Học Toán Bằng Tiếng Anh (Part 8)

Tiếp theo Phần 7: Hệ Thập Phân, Tôi trình bày tiếp Phần 8: Số thập phân (Decimal Numbers.)

The zero and the counting numbers (1, 2, 3,...) make up the set of whole numbers. But not every number is a whole number. Our decimal system lets us write numbers of all types and sizes, using a clever symbol called the decimal point.