## Posts

Showing posts from June 7, 2020

### Circle in the Corner

A regular hexagon ABCDEF has the side length of 6. Circle O is inscribed in the hexagon. The tangent points on AB and AF are G and H respectively. Circle P is inscribed in the corner area sounded by HA, AG, and arc GH. What's the radius of circle P? (Do not use calculator. Let the square root of 3 be 1.73. When submitting the result, keep two digits after decimal point.)

### Triangles in a Grid

Nine dots form a 3 by 3 grid. The distance between any two adjacent dots in the left-right or up-down direction is the same. How many triangles can be formed from this grid by choosing three dots as the vertices?

### Meetup in Classroom

Dr. Hong decides to gather the CMM students for a face-to-face meetup in a classroom, where 90 seats are arranged in a 9 by 10 grid. The distance between two adjacent seats in any row or column is 5 feet. Due to the concern of COVID-19, Dr. Hong wants to keep at least 6 feet distance between any two students. What's the maximum number of students Dr. Hong could bring to the classroom?

### Splitting a Pizza

Leo's mom has made a big (round) pizza for a CMM party. It's Dr. Hong's job to split it. If Dr. Hong cuts one line through the circle, he can split the pizza into two pieces. If Dr. Hong cuts two lines, he can split the pizza into four pieces at most. If Dr. Hong cuts 6 lines, what's the greatest number of pieces can he get? (Dr. Hong cannot stack the pieces before making a cut.)

### GRIT

In the expression STARTUP + GRIT = SUCCESS, each letter represents a single digit number from 0 to 9. Different letters represent different numbers. S and G cannot be zero. What's GRIT?

### Three Composite Numbers

The greatest common factor of three different composite numbers is 21. The product of them is 1,018,710. What's the smallest possible sum of these three numbers?

Warm up: how many possible values for each two-digit number in bold?

JH + 13 = MVP
KD + 35 = MVP

Find the unique solution

DREAM + TEAM = WINNER
BLACK + MAMBA = KOBE24
BLACK + MAMBA = CLUTCH
NY × 17 = LIN
KOBE × 24 = MAMBA
CHICAGO + BULLS = CLASSIC (This one is really hard.)

### Alphametic Warmup

Find the range of each letter in bold:

A + B = C
AB = C
A + B = CD
AA + B = CD
AA + B = CDE
A × B = C
A × B = CD
AA × BB = CDE
AA × BB = CDEF

Find the unique solution

SEND + MORE = MONEY
SMART + MOVE = DOCTOR
TRIAL + ERROR = ASSURE
SMART + MIRACLE = SUCCESS