# day/dydd 245 at 7puzzleblog.com T he Main Challenge

Using the numbers 5, 5 and 10 once each, with + – × ÷ available, list the NINE target numbers from 1-30 that are mathematically possible to achieve. 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 & 7th rows of the playing board contain the following fourteen numbers:

4    6    7    11    16    21    24    27    30    50    70    77    81    84

Which four different numbers 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 ELEVEN different ways to make 245 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 25 and 10 once each, with + – × ÷ available, which are the only THREE 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 245 by inserting 1234 and 5 into the gaps below?

•  (◯+◯)²×◯×(◯–◯) = 245   