# DAY/DYDD 228: T he Main Challenge

You have been given a starting number as well as an end answer. There are seven arithmetical steps in all, but the middle step is missing!

2    ×4    +1    ?    ×5    ÷3    +2    =    7

The missing step involves a single-digit integer (whole number).  Work out this missing step so the final answer will also be 7. 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 & 7th rows of the playing board contain the following fourteen numbers:

2   4   9   11   14   15   22   24   27   30   40   70   72   77

Which four different numbers above have a sum of 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 228 when using Lagrange’s Theorem. How many can you find? The Mathematically Possible Challenge

Using 24 and once each, with + – × ÷ available, which FOUR numbers is it 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 228 by inserting 34, 5 and 6 into the gaps on each line?

•  ◯×(◯²+◯²–◯) = 228
•  ◯×(◯²×◯+double◯) = 228   