# DAY/DYDD 214: T he Main Challenge

By using the numbers 4, 5, 7 and 8 exactly once each, and with the four arithmetical operations + – × ÷ available, can you arrive at the target answer of 12 in two different ways? 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 of the playing board contain the following fourteen numbers:

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

From the list, find FOUR different numbers that total 100. 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 TEN different ways to make 214 when using Lagrange’s Theorem. How many can you find? The Mathematically Possible Challenge

Using 46 and once each, with + – × ÷ available, which are the only THREE numbers it is possible to make from the list below?

5    10    15    20    25    30    35    40    45    50

#5TimesTable The Target Challenge

Can you arrive at 214 by inserting 2610 and 20 into the gaps on each line?

•  (◯+◯)×◯–◯ = 214
•  ◯×◯+◯+double◯ = 214
•  (◯+◯)²–(◯+double◯) = 214   