Summing Consecutive Numbers

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?

Frogs

How many moves does it take to swap over some red and blue frogs? Do you have a method?

The Best Card Trick?

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

Perimeter Possibilities

Stage: 3 Challenge Level:
Imagine two islands with an area of $24$, one with dimensions $6$ by $4$ and the other $12$ by $2$.

Which island has more land by the sea shore?