# DAY/DYDD 191: The Main Challenge

This is a very special challenge personally endorsed by Robert Sun, inventor of the world-famous maths card game, 24game®.

The idea is very simple; to make 24 from the card below by using the four numbers exactly once each, and with + – × ÷ available.

(The three dots in each corner signifies a hard level of challenge) Can you also make 24 from the following two combinations using the same rules?

•  1   5   5   5
•  4   4   7   7 The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 2 up to 84.

The 4th & 5th rows of the playing board contain the following fourteen numbers:

3   6   7   10   16   21   32   35   44   50   54   60   81   84

What is the sum when adding together all the multiples of 7? 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).

Show how you can make 191, in FIVE different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 34 and 12 once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

9    18    27    36    45    54    63    72    81    90

#9TimesTable The Target Challenge

Can you arrive at 191 by inserting 7, 11, 19 and 25 into the gaps on each line?

•  ◯×◯+◯–◯ = 191
•  ◯×◯+double(◯–◯) = 191   