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Resources tagged with smartphone similar to Weekly Problem 22 - 2009:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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Broad Topics > Information and Communications Technology > smartphone

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Power Mad!

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

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Negative Power

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What does this number mean ? Which order of 1, 2, 3 and 4 makes the highest value ? Which makes the lowest ?

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Days and Dates

Stage: 4 Challenge Level: Challenge Level:1

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

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Perfectly Square

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

The sums of the squares of three related numbers is also a perfect square - can you explain why?

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14 Divisors

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

What is the smallest number with exactly 14 divisors?

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Expenses

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?

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Dozens

Stage: 3 Challenge Level: Challenge Level:1

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

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Areas and Ratios

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.

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2-digit Square

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

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Always Perfect

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

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How Many Miles to Go?

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A car's milometer reads 4631 miles and the trip meter has 173.3 on it. How many more miles must the car travel before the two numbers contain the same digits in the same order?

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Make 37

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

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Odd Differences

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.

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Plus Minus

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you explain the surprising results Jo found when she calculated the difference between square numbers?

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Pair Products

Stage: 4 Challenge Level: Challenge Level:1

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

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The Root of the Problem

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

Find the sum of the series.

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Terminology

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Triangle ABC is isosceles while triangle DEF is equilateral. Find one angle in terms of the other two.

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Tet-trouble

Stage: 4 Challenge Level: Challenge Level:1

Show that is it impossible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units...

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Elevenses

Stage: 3 Challenge Level: Challenge Level:1

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

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Legs Eleven

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?

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Cuboids

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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Largest Product

Stage: 3 and 4 Challenge Level: Challenge Level:1

Which set of numbers that add to 10 have the largest product?

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Take Three from Five

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

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Salinon

Stage: 4 Challenge Level: Challenge Level:1

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

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Going Round in Circles

Stage: 3 Challenge Level: Challenge Level:1

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

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Sissa's Reward

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...

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What's Possible?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

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Repetitiously

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

The number 2.525252525252.... can be written as a fraction. What is the sum of the denominator and numerator?

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Nicely Similar

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?

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Trapezium Four

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

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Handshakes

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?

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Matchless

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

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CD Heaven

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at. . . .

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Picturing Square Numbers

Stage: 3 Challenge Level: Challenge Level:1

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

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Squares in Rectangles

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Areas of Parallelograms

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you find the area of a parallelogram defined by two vectors?

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Marbles in a Box

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

In a three-dimensional version of noughts and crosses, how many winning lines can you make?

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Circle-in

Stage: 4 Challenge Level: Challenge Level:1

A circle is inscribed in a triangle which has side lengths of 8, 15 and 17 cm. What is the radius of the circle?

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Shady Symmetry

Stage: 3 Challenge Level: Challenge Level:1

How many different symmetrical shapes can you make by shading triangles or squares?

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Searching for Mean(ing)

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?

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Curvy Areas

Stage: 4 Challenge Level: Challenge Level:1

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

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An Unusual Shape

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Can you maximise the area available to a grazing goat?

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Litov's Mean Value Theorem

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Start with two numbers. This is the start of a sequence. The next number is the average of the last two numbers. Continue the sequence. What will happen if you carry on for ever?

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Painted Cube

Stage: 3 Challenge Level: Challenge Level:1

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

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Gutter

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?

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Sending a Parcel

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

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Cuboid Challenge

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?

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Fence It

Stage: 3 Challenge Level: Challenge Level:1

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

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On the Edge

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Here are four tiles. They can be arranged in a 2 by 2 square so that this large square has a green edge. If the tiles are moved around, we can make a 2 by 2 square with a blue edge... Now try to. . . .

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Orbiting Billiard Balls

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?