# Place Value, Integers, Ordering and Rounding Stage 3 - Short Problems

### Central Sum

##### Stage: 3 Short Challenge Level:

Weekly Problem 53 - 2011
Find a number between 100 and 999 that has its middle digit equal to the sum of the other two digits. Can you find all possibilities?

### Weekly Problem 17 - 2008

##### Stage: 3 and 4 Challenge Level:

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

### Weekly Problem 21 - 2008

##### Stage: 3 and 4 Challenge Level:

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

### Weekly Problem 27 - 2008

##### Stage: 3 and 4 Challenge Level:

In the diagram in the question, how many squares, of any size, are there whose entries add up to an even total?

### Weekly Problem 47 - 2008

##### Stage: 3 Challenge Level:

Can you solve this magic square?

### Tinker, Tailor

##### Stage: 3 Short Challenge Level:

Weekly Problem 4 - 2009
Bilbo and Frodo use a rhyme as they count their own cherry stones - where will they finish if they count all stones together?

### Debt Recovery

##### Stage: 3 Short Challenge Level:

Weekly Problem 7 - 2009
Tony and Tina can't work out which of them owes what to the other. Can you?

### Baby's Blocks

##### Stage: 3 Short Challenge Level:

Weekly Problem 8 - 2009
How many ways can Gill, the baby, arrange the letters in her name?

### Loose Change

##### Stage: 3 Short Challenge Level:

Weekly Problem 10 - 2009
In how many ways can you give change for a ten pence piece?

### Mathematical Ages

##### Stage: 3 Short Challenge Level:

Weekly Problem 16 - 2009
Arrange these three famous mathematicians in order with the shortest-lived first.

### Quiz Questions

##### Stage: 3 Short Challenge Level:

Weekly Problem 25 - 2009
Jack does a 20-question quiz. How many questions didn't he attempt?

### Weekly Problem 32 - 2009

##### Stage: 3 Short Challenge Level:

I have a max/min thermometer in my greenhouse. What were the maximum and minimum temperatures recorded when I looked at it on Wednesday evening?

### Weekly Problem 52 - 2009

##### Stage: 2 and 3 Short Challenge Level:

Gar the Magician plays a card trick on his friends Kan and Roo. Can you work out his trick and find out the sum on Kan's cards?

### Half Way

##### Stage: 3 Short Challenge Level:

Weekly Problem 24 - 2010
Can you find a number that is half way between these two fractions?

### Alberta's Age

##### Stage: 2 and 3 Short Challenge Level:

Weekly Problem 26 - 2011
Alberta won't reveal her age. Can you work it out from these clues?

### Double with 1-9

##### Stage: 3 Short Challenge Level:

Weekly Problem 31 - 2011
Can you find a number and its double using the digits $1$ to $9$ only once each?

### Filling Morecambe Bay

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 19 - 2016
"It would take 20 million years to fill Morecambe Bay from a bath tap". What does this imply is the approximate capacity of Morecambe Bay?

### Very Long Line

##### Stage: 3 Short Challenge Level:

Weekly Problem 46 - 2016
If the line on the right were 0.2mm thick, how long would it need to be to cover an area of one square metre?