# DAY/DYDD 233: T he Main Challenge

Firstly, write down three separate lists only containing numbers in the range 1 to 100:

•  List 1 – multiples of 9
•  List 2 – factors of 108
•  List 3 – triangular numbers

Part 1: Which is the only number present on all three lists?

Part 2: List the eight other numbers that are on exactly two of the lists?

Part 3: How many DIFFERENT numbers are written on the three lists? The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from up to 84.

The 2nd & 4th rows of the playing board contain the following fourteen numbers:

3   8   10   17   28   32   35   44   48   54   55   60   63   64

From the list, what is the sum of the even numbers? The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every positive integer can be made by adding up to four square numbers.

For example, 7 can be made by 2²+1²+1²+1² (or 4+1+1+1).

There are EIGHT different ways to make 233 when using Lagrange’s Theorem. How many of them can you find? The Mathematically Possible Challenge

Using 24 and once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

2    3    5    7    11    13    17    19    23    29 The Target Challenge

Can you arrive at 233 by inserting 11, 12, 13, 14 and 15 into the gaps below?

•  6×◯+5×◯+4×◯+3×◯–◯ = 233   