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?

Magic Caterpillars

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

Plum Tree

Label this plum tree graph to make it totally magic!

Rectangle Outline Sudoku

Stage: 3 and 4 Challenge Level:

Invented by Henry Kwok

Rules of Rectangle Outline Sudoku

This Sudoku variant has two additional rules.

As usual, the object of the puzzle is to fill in the whole 9x9 grid with numbers 1 through 9 so that each row, each column and each box must contain all the nine different numbers 1 to 9 irrespective of order.

The two additional rules of the variant are as follows:

Each of the two main diagonals of the puzzle must have the numbers 1 to 9.
Within the 9x9 pattern there is a highlighted "rectangle" with its width four and length six cells respectively. Each width of the "rectangle" outline must contain all the four numbers 1 to 4. Similarly, each length of the "rectangle" must contain all the six numbers 1 to 6.