# day/dydd 202 at 7puzzleblog.com

Th e Main Challenge

If you added together the first seven odd numbers that do not contain a 3, 5 or 7 as part of their number or are not multiples of 3, 5 or 7, what is your answer?

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 1st & 3rd rows of the playing board contain the following fourteen numbers:

2   9   13   14   15   22   25   36   40   42   45   66   72   80

What is the average of the three consecutive numbers listed above?

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 THIRTEEN different ways to make 202 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Using 57 and 11 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

7    14    21    28    35    42    49    56    63    70

#7TimesTable

The Target Challenge

Can you arrive at 202 by inserting 7813 and 14 into the gaps on each line?

•  ◯×◯+◯×◯ = 202
•  ◯²+(◯–◯)²–double◯ = 202