# DAY/DYDD 109: T he Main Challenge

Last chance to get all seven correct. Be careful as there may be one or two tricky ones!

1.  (1 – 2) – (3 – 4) = ?
2.  4 ÷ 0.5 = ?
3.  What is 25 less than the product of 20 and 10?
4.  How do you write “Six and six hundredths” in decimal format?
5.  4,000 × 0.02 = ?
6.  Find 10% of £13.
7.  What is 31 × 15? 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 1st & 2nd rows contain the following fourteen numbers:

2   8   9   14   15   17   22   28   40   48   55   63   64   72

What is the sum of the odd 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 FIVE ways of making 109 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 14 and once each, with + – × ÷ available, which TWO numbers is it possible to make from the list below?

7    14    21    28    35    42    49    56    63    70

#7TimesTable

The Target Challenge

Can you arrive at 109 by inserting 3, 8, 10 and 12 into the gaps on both lines?

•  ◯×◯–(◯+◯) = 109
•  ◯×◯+◯+◯ = 109   