Problem of the Week #2

Amy passed around a basket of strawberries to the girls at her party. Before the party she ate 5 strawberries and gave a friend 3. Eight girls arrived at the party. The first girl took a strawberry, the second girl took 3 strawberries, the third girl took 5 strawberries and so on. After the last girl took her strawberries, the basket was empty. How many strawberries were in the basket at the beginning?

Problem of the Week #1

A palindrome is a word or phrase that is spelled the same forward and backward. My favorite palindromes are "I, madam, I made radio. So I dared! Am I mad, am I?" and "Rats live on no evil star."

A palindrome number is one which would have the same value if it were turned front to back. The numbers 12,321 and 5,775 are examples.

Problem: Find a palindrome number x such that

where if A is the first digit of x, B is the second digit, and C is the third digit of x, then

and