# DAY/DYDD 225: T he Main Challenge

Each of the five numbers below is the product of two prime numbers:

15     35     77     143     323

Which is the odd one out, and why? 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 5th & 6th rows of the playing board contain the following fourteen numbers:

5   6   7   12   16   18   20   21   33   49   50   56   81   84

What is the sum of 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).

There are FOURTEEN different ways to make 225 when using Lagrange’s Theorem. How many can you find? The Mathematically Possible Challenge

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

15    30    45    60    75    90    105    120    135    150

#15TimesTable The Target Challenge

Can you arrive at 225 by inserting 345 and 9 into the gaps on each line?

•  (◯–◯)×◯×◯² = 225   (there are 2 ways!)
•  (◯+◯+◯–◯)² = 225   