# DAY/DYDD/GIORNO/NAP 192: T he Main Challenge

This is a number puzzle taken from my scrapbook of brainteasers, a favourite of mine, and used regularly as a mental maths starter in my workshops over the years!

You have a 6-sector dartboard containing the numbers 16 17 23 24 39 and 40. Your task is to achieve EXACTLY 100 when adding your scores together. This can be done by throwing any number of darts, each of which can land in any sector more than once. There is only ONE way of achieving a score of 100. How can it be done? 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 4th & 5th rows of the playing board contain the following fourteen numbers:

3   6   7   10   16   21   32   35   44   50   54   60   81   84

List two pairs of numbers that differ by 19. 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).

Show how you can make 192, in just TWO different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 34 and 12 once each, with + – × ÷ available, which are the only TWO numbers is it 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 192 by inserting 4, 6, 8 and 10 into the gaps on each line?

•  (◯+◯)×(◯+◯) = 192
•  (◯×◯–◯)×◯ = 192
•  double(◯×(◯+◯))–◯ = 192   