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#### Resources tagged with smartphone similar to Happy Numbers:

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Broad Topics > Information and Communications Technology > smartphone

### 1 Step 2 Step

##### Age 11 to 14 Challenge Level:

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

### Pair Products

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

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

### Who Is the Fairest of Them All ?

##### Age 11 to 14 Challenge Level:

Explore the effect of combining enlargements.

### Think of Two Numbers

##### Age 11 to 14 Challenge Level:

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

### What's Possible?

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

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

### Keep it Simple

##### Age 11 to 14 Challenge Level:

Can all unit fractions be written as the sum of two unit fractions?

### Largest Product

##### Age 11 to 14 Challenge Level:

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

### Children at Large

##### Age 11 to 14 Challenge Level:

There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?

### Painted Cube

##### Age 11 to 14 Challenge Level:

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?

### Marbles in a Box

##### Age 11 to 14 Challenge Level:

How many winning lines can you make in a three-dimensional version of noughts and crosses?

### Route to Infinity

##### Age 11 to 14 Challenge Level:

Can you describe this route to infinity? Where will the arrows take you next?

### Mirror, Mirror...

##### Age 11 to 14 Challenge Level:

Explore the effect of reflecting in two parallel mirror lines.

### Handshakes

##### Age 11 to 14 Challenge Level:

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

### Searching for Mean(ing)

##### Age 11 to 14 Challenge Level:

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?

### Picturing Square Numbers

##### Age 11 to 14 Challenge Level:

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

### Litov's Mean Value Theorem

##### Age 11 to 14 Challenge Level:

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

### Make 37

##### Age 7 to 14 Challenge Level:

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.

### Odd Differences

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

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.

### Tiny Nines

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

Find the decimal equivalents of the fractions one ninth, one ninety ninth, one nine hundred and ninety ninth etc. Explain the pattern you get and generalise.

### Consecutive Negative Numbers

##### Age 11 to 14 Challenge Level:

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

### Weights

##### Age 11 to 14 Challenge Level:

Different combinations of the weights available allow you to make different totals. Which totals can you make?

### Squares in Rectangles

##### Age 11 to 14 Challenge Level:

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?

### Ben's Game

##### Age 11 to 14 Challenge Level:

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

### Differences

##### Age 11 to 14 Challenge Level:

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

### Sweet Shop

##### Age 11 to 14 Challenge Level:

Five children went into the sweet shop after school. There were choco bars, chews, mini eggs and lollypops, all costing under 50p. Suggest a way in which Nathan could spend all his money.

### Do You Feel Lucky?

##### Age 11 to 14 Challenge Level:

Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?

### Always Perfect

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

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

### Perfectly Square

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

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

### Counting Factors

##### Age 11 to 14 Challenge Level:

Is there an efficient way to work out how many factors a large number has?

### Sending a Parcel

##### Age 11 to 14 Challenge Level:

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

### Days and Dates

##### Age 11 to 14 Challenge Level:

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

### One and Three

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

Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .

### Eight Hidden Squares

##### Age 7 to 14 Challenge Level:

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

### On the Edge

##### Age 11 to 14 Challenge Level:

If you move the tiles around, can you make squares with different coloured edges?

### Beelines

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

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

### Can They Be Equal?

##### Age 11 to 14 Challenge Level:

Can you find rectangles where the value of the area is the same as the value of the perimeter?

### How Much Can We Spend?

##### Age 11 to 14 Challenge Level:

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

##### Age 11 to 14 Challenge Level:

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

### Areas of Parallelograms

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

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

### An Unusual Shape

##### Age 11 to 14 Challenge Level:

Can you maximise the area available to a grazing goat?

### Plus Minus

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

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

### Cuboid Challenge

##### Age 11 to 14 Challenge Level:

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

### Sissa's Reward

##### Age 11 to 14 Challenge Level:

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

### Summing Consecutive Numbers

##### Age 11 to 14 Challenge Level:

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

### Legs Eleven

##### Age 11 to 14 Challenge Level:

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

### Mixing More Paints

##### Age 11 to 14 Challenge Level:

Is it always possible to combine two paints made up in the ratios 1:x and 1:y and turn them into paint made up in the ratio a:b ? Can you find an efficent way of doing this?

### Number Daisy

##### Age 11 to 14 Challenge Level:

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

### Consecutive Numbers

##### Age 7 to 14 Challenge Level:

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

### Rule of Three

##### Age 11 to 14 Challenge Level:

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

### How Many Miles to Go?

##### Age 11 to 14 Challenge Level:

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?