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#### Resources tagged with Working systematically similar to PCDF:

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### There are 74 results

Broad Topics > Using, Applying and Reasoning about Mathematics > Working systematically

### Function Pyramids

##### Age 16 to 18 Challenge Level:

A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?

### Interpolating Polynomials

##### Age 16 to 18 Challenge Level:

Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.

### Latin Squares

##### Age 11 to 18

A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.

### All-variables Sudoku

##### Age 11 to 18 Challenge Level:

The challenge is to find the values of the variables if you are to solve this Sudoku.

### Spot the Card

##### Age 14 to 16 Challenge Level:

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

### Star Product Sudoku

##### Age 11 to 16 Challenge Level:

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

### Twin Line-swapping Sudoku

##### Age 14 to 16 Challenge Level:

A pair of Sudoku puzzles that together lead to a complete solution.

### Impuzzable

##### Age 16 to 18

This is about a fiendishly difficult jigsaw and how to solve it using a computer program.

### LCM Sudoku

##### Age 14 to 16 Challenge Level:

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

### Constellation Sudoku

##### Age 14 to 18 Challenge Level:

Special clue numbers related to the difference between numbers in two adjacent cells and values of the stars in the "constellation" make this a doubly interesting problem.

### Purr-fection

##### Age 16 to 18 Challenge Level:

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

### The Best Card Trick?

##### Age 11 to 16 Challenge Level:

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

### Difference Sudoku

##### Age 14 to 16 Challenge Level:

Use the differences to find the solution to this Sudoku.

### Twin Corresponding Sudokus II

##### Age 11 to 16 Challenge Level:

Two sudokus in one. Challenge yourself to make the necessary connections.

### Intersection Sudoku 1

##### Age 11 to 16 Challenge Level:

A Sudoku with a twist.

### Magnetic Personality

##### Age 7 to 16 Challenge Level:

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

### Ratio Sudoku 2

##### Age 11 to 16 Challenge Level:

A Sudoku with clues as ratios.

### LOGO Challenge - the Logic of LOGO

##### Age 11 to 16 Challenge Level:

Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?

### Integrated Sums Sudoku

##### Age 11 to 16 Challenge Level:

The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .

### Seasonal Twin Sudokus

##### Age 11 to 16 Challenge Level:

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

### LOGO Challenge - Sequences and Pentagrams

##### Age 11 to 18 Challenge Level:

Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?

##### Age 11 to 16 Challenge Level:

Four small numbers give the clue to the contents of the four surrounding cells.

### The Great Weights Puzzle

##### Age 14 to 16 Challenge Level:

You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?

### Pole Star Sudoku 2

##### Age 11 to 16 Challenge Level:

This Sudoku, based on differences. Using the one clue number can you find the solution?

##### Age 11 to 16 Challenge Level:

Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.

### LCM Sudoku II

##### Age 11 to 18 Challenge Level:

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

### Bochap Sudoku

##### Age 11 to 16 Challenge Level:

This Sudoku combines all four arithmetic operations.

### Colour Islands Sudoku 2

##### Age 11 to 18 Challenge Level:

In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.

### Twin Corresponding Sudoku III

##### Age 11 to 16 Challenge Level:

Two sudokus in one. Challenge yourself to make the necessary connections.

### Rectangle Outline Sudoku

##### Age 11 to 16 Challenge Level:

Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.

### Rainstorm Sudoku

##### Age 14 to 16 Challenge Level:

Use the clues about the shaded areas to help solve this sudoku

### Difference Dynamics

##### Age 14 to 18 Challenge Level:

Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?

### Bent Out of Shape

##### Age 14 to 18 Challenge Level:

An introduction to bond angle geometry.

### A Long Time at the Till

##### Age 14 to 18 Challenge Level:

Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?

### Advent Calendar 2011 - Secondary

##### Age 11 to 18 Challenge Level:

Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.

### I've Submitted a Solution - What Next?

##### Age 5 to 18

In this article, the NRICH team describe the process of selecting solutions for publication on the site.

### Olympic Logic

##### Age 11 to 16 Challenge Level:

Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

##### Age 11 to 16 Challenge Level:

This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.

### Magic W

##### Age 14 to 16 Challenge Level:

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

### Smith and Jones

##### Age 14 to 16 Challenge Level:

Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!

### Pole Star Sudoku

##### Age 14 to 18 Challenge Level:

A Sudoku based on clues that give the differences between adjacent cells.

### Twin Corresponding Sudoku

##### Age 11 to 18 Challenge Level:

This sudoku requires you to have "double vision" - two Sudoku's for the price of one

### Warmsnug Double Glazing

##### Age 14 to 16 Challenge Level:

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

### Exhaustion

##### Age 16 to 18 Challenge Level:

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

### The Naked Pair in Sudoku

##### Age 7 to 16

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

### Intersection Sums Sudoku

##### Age 7 to 16 Challenge Level:

A Sudoku with clues given as sums of entries.

### Plum Tree

##### Age 14 to 18 Challenge Level:

Label this plum tree graph to make it totally magic!

### Instant Insanity

##### Age 11 to 18 Challenge Level:

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

### Olympic Magic

##### Age 14 to 16 Challenge Level:

in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?