Angela’s Favorite Book

Angela’s favorite book is “The Secret of Cacklefur Castle”. The book has 109 pages. If the pages are numbered consecutively starting from 1. How many times the digit 0 shows up in the page numbers?

Starting with a Random Number

Pick any number between 1 and 10. Subtract 2. Add 3. Subtract 5. Add 7. Subtract the original number. What’s the largest possible value of the resulting number?

Mixing Additions and Subtractions

 Compute: 2 - 4 + 6 - 8 + 10 - 12 + 14 - 16 + 18.

Adding 16 Numbers

Without using a calculator, calculate: 1 + 2 + 8 + 9 + 11 + 12 + 18 + 19 + 21 + 22 + 28 + 29 + 31 + 32 + 38 + 39 = ?

Sum of Digits

What's the sum of digits of 999,999,999 × 666,666?

Maximize the Expression

Fill in the blanks of the expression 1 _ 2 _ 3 _ 2 _ 1 with all four basic arithmetic operators, and then add one pair of parentheses. What's the maximum value of the resulting expression?

Dr. Hong's Magic Number

Dr. Hong has a magic number ABACDD that satisfies the following conditions:

1. ABACDD = EF × BE × GD; 
2. BE × GD = EGHF; 
3. EF, BE, and GD are prime numbers;  
4. A, B, C, D, E, F, G, H represent eight different single-digit non-zero integers. 

what is Dr. Hong's magic number ABACDD?