Describing patterns and sequences

problem
A shapely network

Age

7 to 11

Challenge level

Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.
problem
The tomato and the bean

Age

5 to 7

Challenge level

At the beginning of May, Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?
problem
A calendar question

Age

7 to 11

Challenge level

July 1st 2001 was on a Sunday. July 1st 2002 was on a Monday. When did July 1st fall on a Monday again?
problem
Next number

Age

7 to 11

Challenge level

Find the next number in this pattern: 3, 7, 19, 55 ...
problem
1 step 2 step

Age

11 to 14

Challenge level

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
problem
Paving paths

Age

11 to 14

Challenge level

How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?
problem
Millennium man

Age

7 to 11

Challenge level

Liitle Millennium Man was born on Saturday 1st January 2000 and he will retire on the first Saturday 1st January that occurs after his 60th birthday. How old will he be when he retires?
problem
Pyramid numbers

Age

7 to 11

Challenge level

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?
problem
Days and dates

Age

11 to 14

Challenge level

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
problem
Little squares

Age

5 to 7

Challenge level

Look at the squares in this problem. What does the next square look like? I draw a square with 81 little squares inside it. How long and how wide is my square?