Working systematically

There are 604 NRICH Mathematical resources connected to Working systematically
Reach 100
problem
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Reach 100

Age
7 to 11
Challenge level
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Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Tilted Squares
problem
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Tilted squares

Age
11 to 14
Challenge level
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It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Orange Drink
problem
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Orange drink

Age
7 to 11
Challenge level
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A 750 ml bottle of concentrated orange squash is enough to make fifteen 250 ml glasses of diluted orange drink. How much water is needed to make 10 litres of this drink?

Triangles all Around
problem
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Triangles all around

Age
7 to 11
Challenge level
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Can you find all the different triangles on these peg boards, and find their angles?
Squares in rectangles
problem
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Squares in rectangles

Age
11 to 14
Challenge level
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A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?
What's in the Box?
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What's in the box?

Age
7 to 11
Challenge level
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This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

Opposite vertices
problem
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Opposite vertices

Age
11 to 14
Challenge level
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Can you recreate squares and rhombuses if you are only given a side or a diagonal?

Maze 100
problem
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Maze 100

Age
7 to 11
Challenge level
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Can you go through this maze so that the numbers you pass add to exactly 100?
Wonky Watches
problem
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Wonky watches

Age
7 to 11
Challenge level
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Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

Multiplication Squares
problem
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Multiplication squares

Age
7 to 11
Challenge level
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Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.