# day/dydd 133 at 7puzzleblog.com T he Main Challenge

Group these ten numbers into five pairs so that the difference between the two numbers in each pair is divisible by 7:

6    17    28    37    45    58    64    78    83    98 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 3rd & 6th rows contain the following fourteen numbers:

5   12   13   18   20   25   33   36   42   45   49   56   66   80

From the list, what is the sum of the multiples of 7? 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 SEVEN ways of making 133 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 36 and 10 once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

8    16    24    32    40    48    56    64    72    80

#8TimesTable

The Target Challenge

Can you arrive at 133 by inserting 10, 11, 13 and 20 into the gaps on each line?

•  ◯×◯+◯–◯ = 133
•  ◯×◯+√(◯–◯) = 133   