# DAY/DYDD/GIORNO/NAP 209: T he Main Challenge

This is very famous in Japan, having been an integral part of a TV advert for Google’s Nexus 7 tablet a few years ago.  Click this YouTube link for a browse.

Using the numbers 1, 1, 5 and 8 exactly once each, with + – × and ÷ available, can you beat this tricky Japanese challenge by arriving at the target answer of 10? 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 2nd & 5th rows of the playing board contain the following fourteen numbers:

6   7   8   16   17   21   28   48   50   55   63   64   81   84

How many more square numbers than prime numbers are listed above? 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 NINE different ways to make 209 when using Lagrange’s Theorem. How many can you find? The Mathematically Possible Challenge

Using 57 and 11 once each, with + – × ÷ available, which are the only TWO numbers 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 209 by inserting 2, 7, 9 and 12 into the gaps on each line?

•  ◯×◯×◯–◯ = 209
•  (◯+◯)×(◯+◯) = 209   