The Fairy-Tale-King invited you to sit down in front of him… “Design for me, a magical castle with beautiful towers.” he demanded. He has enough money to pay for ten floors and you need to distribute these ten floors any way you like between your towers. “However”, he whispered, “None of the towers can be the same height!” For example, you could build three towers of height 4,5,1 but you could not build four towers of heights 1,3,5,1 because two towers are of height 1.
How many different possible ways can you build the towers? Submit your answer as a picture or a table.
1, 2, 3, 4
Using the digits 1, 2, 3 and 4 and +, – , x and ÷ symbols make the numbers from 1 to 30.
Each of the numbers has to be used every time, for example 1 + 2 + 3 + 4 = 10.
Which numbers from 1 – 30 can be written as the sum of 2 consecutive numbers?
What do you notice about these numbers?
What two consecutive whole numbers add together to make 101, 4323 or 54 307? How do you know?
Extend to the sums of 3, 4, 5… consecutive numbers
- Using four different integers and the x symbol make the highest possible result.
All the integers have to be used. For example: 3, 7, 5, 1 gives 157 x 3 = 471 or 37 x 51 =1887.
- Now chose four other integers and make the largest result using only multiplication.
- What conclusions can you make?
- What predictions can you make about 5, 6, … digits?