### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Tea Cups

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

### 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?

# Twin Corresponding Sudoku III

##### Stage: 3 and 4 Challenge Level:

Invented by Henry Kwok

### Rules of Twin Corresponding Sudoku

The object of this sudoku variant is to fill in each twin puzzle with numbers 1 to 9 so that each row, each column, and each of the nine 3x3 boxes contain all the nine different numbers 1 to 9.

This variant consists of a pair of linked standard sudoku puzzles each with some starting digits. To get a complete solution for the twin puzzles, we have to solve each twin puzzle with the usual sudoku strategy but we can only get the complete solution of the twin puzzles by substituting the corresponding values of the digits from one twin sudoku into the other.

So, for example, we find that in r4c9, that is row 4 column 9, twin A contains the number 7 and twin B contains the number 4. This means that wherever 7 appears in twin A, it should be substituted by 4 in the corresponding position in twin B and wherever there is a 4 in Twin B there is a 7 in twin A. This immediately gives you some more starting digits in each twin!