Counting on Letters

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

Purr-fection

What is the smallest perfect square that ends with the four digits 9009?

Exhaustion

Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2

Addition Equation Sudoku

Stage: 3, 4 and 5 Challenge Level:

By Henry Kwok

Rules of Addition Equation Sudoku

Like the standard sudoku, this sudoku has the basic rule:

Every row, every column and every 3x3 box in the grids contains the digits 1 through 9.

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the 9x9 grid. At the bottom and right side of the 9x9 grid are numbers, each of which is the sum of a column or row of unknown digits marked by asterisks.

In this puzzle, a set of 17 equations can be formed from the columns and rows of unknown digits and constants. For example, in the fourth and fifth columns beginning from the left of the 9x9 grid, the following equations can be formed:

$* + * + * = 6$ and

$* + * = 9$.

In the eighth and ninth rows beginning from the top of the 9x9 grid, the following equations can be formed:

$* + * + * = 11$ and

$* + * = 13$.

After solving all the equations, the puzzle is solved by the usual sudoku technique and strategy.

Combinatorics. Visualising. Working systematically. Networks/Graph Theory. Manipulating algebraic expressions/formulae. Games. Factors and multiples. Quadratic equations. Mathematical reasoning & proof. Simultaneous equations.