# 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.

### Reverse Ages

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

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

### Central Sum

##### Age 11 to 14 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

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

Can you solve this magic square?

### Negative Dice

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

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

### Rough Rectangle

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

What is the smallest possible area that this rectangle could have?

### Debt Recovery

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

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

### Count Back

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

How well can you count back from sixty thousand?

### Loose Change

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

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

### Mathematical Ages

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

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

### Quiz Questions

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

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

### Mini Kakuro

##### Age 11 to 14 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?

### Highs and Lows

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

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

### Even Squares

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

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

### Tick Tock

##### Age 11 to 14 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?

### Double with 1 to 9

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

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

### Paying the Bill

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

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

### Digital Book

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

If it takes 852 digits to number all the pages of a book, what is the number of the last page?

### Missing 9s

##### Age 11 to 14 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?

### Digit Sum Puzzle

##### Age 11 to 14 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

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

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

### Alberta's Age

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

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

### Repeat Product

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

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

### Sum Up

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

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

### Pros and Cons

##### Age 14 to 16 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?

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

How many digits are there in this product?

### How Many Gorillas?

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

If the numbers in this news article have been estimated, then what is the largest number of gorillas that there could have been 10 years ago?

### Number Crunch

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

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

### Digital Counter

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

When the numbers from 1 to 1000 are written on a blackboard, which digit appears the most number of times?