# DAY/DYDD/GIORNO/NAP 29: The Main Challenge

What is the 7th 2-digit whole number that is both a multiple of 5 AND contains the letter ‘F’ when written in English? 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 3rd & 6th rows contain the following fourteen numbers:

5   12   13   18   20   25   33   36   42   45   49   56   66   80

How many pairs of numbers have a difference of 24? 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 TWO ways of making 29 when using Lagrange’s Theorem. Can you find them both? The Mathematically Possible Challenge

Using 26 and 11 once each, with + – × ÷ available, which are the only TWO 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 29 by inserting 2, 3, 4 and 5 into the gaps on each line?

•  (◯+◯)×+◯ = 29   (there are two ways)
•  ◯×◯×◯+◯ = 29
•  ◯²+◯×◯–◯ = 29   