# Are You Sure?

In this feature you are invited to explore a variety of problems, and are then asked to construct convincing arguments to explain what you have discovered.  You will also be introduced to the symbols $\implies$ and $\iff$ and be challenged to use these to create true statements.

The last day for sending in your solutions to the live problems is Monday 16 May.

### Maxi Pyramid

##### Age 11 to 16Challenge Level
What is the largest number you can obtain at the top of this pyramid?

### Positive Differences

##### Age 11 to 16Challenge Level
Can you fill the circles with the numbers 1 to 6?

### Sliding Rectangleslive

##### Age 11 to 16Challenge Level
Which of the two rectangles has the greater area?

### 11x11 Square

##### Age 11 to 16Challenge Level
Here's a neat trick you can do with an 11 by 11 square...

### River Crossing

##### Age 11 to 18Challenge Level
There is nothing half so much worth doing as simply messing about in boats...

### Isosceles Seven

##### Age 14 to 16Challenge Level
Is it possible to find the angles in this rather special isosceles triangle?

### The Tour De Clochemerle

##### Age 14 to 18Challenge Level
Can you work out where these 5 riders came in a not-quite-so-famous bike race?

### Iffy Logiclive

##### Age 14 to 18Challenge Level
Can you rearrange the cards to make a series of correct mathematical statements?

### IFFY Triangles

##### Age 14 to 18Challenge Level
Can you prove these triangle theorems both ways?