# Place Value, Integers, Ordering and Rounding - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Place Value, Integers, Ordering and Rounding.

Printable worksheets containing selections of these problems are available here:

 Stage 3 ★ Sheet 1 Solutions Sheet 2 Solutions Sheet 3 Solutions

### Paying the Bill

##### KS 3 Short Challenge Level:

Gill and I went out to lunch. We agreed to split the total cost equally. How much did I owe Gill?

### Mathematical Ages

##### KS 3 Short Challenge Level:

Arrange these three famous mathematicians in order with the shortest-lived first.

### Quiz Questions

##### KS 3 Short Challenge Level:

Jack does a 20-question quiz. How many questions didn't he attempt?

### Mini Kakuro

##### KS 3 Short Challenge Level:

The sum of each column and row in this grid give the totals as shown. What number goes in the starred square?

### Reverse Ages

##### KS 3 Short Challenge Level:

When is the next time that Brian's age will be the reverse of his father's age?

### Highs and Lows

##### KS 3 Short Challenge Level:

What were the maximum and minimum temperatures recorded in my max/min thermometer?

### Central Sum

##### KS 3 Short Challenge Level:

Can you find numbers between 100 and 999 that have a middle digit equal to the sum of the other two digits?

### Different Magic Square

##### KS 3 Short Challenge Level:

Can you solve this magic square?

### Count Back

##### KS 3 Short Challenge Level:

How well can you count back from sixty thousand?

### Negative Dice

##### KS 3 Short Challenge Level:

If the odd numbers on two dice are made negative, which of the totals cannot be achieved?

### Debt Recovery

##### KS 3 Short Challenge Level:

Tony and Tina can't work out which of them owes what to the other. Can you?

### Tick Tock

##### KS 3 Short Challenge Level:

Tick's watch is slow and Tock's watch is fast. How long is it before their watches differ by an hour?

### Loose Change

##### KS 3 Short Challenge Level:

In how many ways can you give change for a ten pence piece?

### Sum Up

##### KS 3 Short Challenge Level:

David listed ten consecutive numbers and removed one of them. Which number did he remove?

### Missing 9s

##### KS 3 Short Challenge Level:

Sara makes a list of the whole numbers that do not contain any 9s. What is the 300th number on her list?

### Itchy's Fleas

##### KS 3 Short Challenge Level:

Itchy the dog has a million fleas. How many fleas might his shampoo kill?

### Even Squares

##### KS 3 Short Challenge Level:

Can you find squares within a number grid whose entries add up to an even total?

### Alberta's Age

##### KS 3 Short Challenge Level:

Alberta won't reveal her age. Can you work it out from these clues?

### Double with 1 to 9

##### KS 3 Short Challenge Level:

Can you find a number and its double using the digits $1$ to $9$ only once each?

### Repeat Product

##### KS 3 Short Challenge Level:

Can you work out the value of P+Q+R in the multiplication shown?

### Digit Sum Puzzle

##### KS 3 Short Challenge Level:

Let N be the smallest positive integer whose digits add up to 2015. What is the sum of the digits of N+1?

### Equal Length Powers

##### KS 4 Short Challenge Level:

How many positive integers $n$ exist for which $n^2$ has the same number of digits as $n^3$?

### Pros and Cons

##### KS 4 Short Challenge Level:

If p is a positive integer and q is a negative integer, which of these expressions is the greatest?

### How Many Digits?

##### KS 4 Short Challenge Level:

How many digits are there in this product?

### Number Crunch

##### KS 4 Short Challenge Level:

Create 24 numbers from four digits. Why is 101 always a factor of their sum?