# DAY/DYDD/GIORNO/NAP 171: T he Main Challenge

You have the same starting number and final answer, both 22.

There are 10 arithmetical steps altogether but the 10th, and final, step is missing. If this final step involves a whole number, what should it be to make the final answer 22?

+2   ÷6   ×4   3   ×2   +4   ÷5   +6   ×2   ?   =   22 The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from up to 84.

The 3rd & 5th rows contain the following fourteen numbers:

6   7   13   16   21   25   36   42   45   50   66   80   81   84

List three sets of three numbers that all have a sum of 100, the numbers in each set must be different. The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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).

Show how you can make 171, in TEN different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 46 and 10 once each, with + – × ÷ available, which are the only TWO target numbers it is possible to make from the list below?

10    20    30    40    50    60    70    80    90    100

#10TimesTable The Target Challenge

Can you arrive at 171 by inserting 3, 69 and 10 into the gaps on each line?

•  ◯×◯×◯–◯ = 171
•  (◯+◯+◯)×◯ = 171   