# day/dydd 58 at 7puzzleblog.com

T he Main Challenge

Starting from 1, find the sum of the first SEVEN whole numbers that do not contain a 3, 5 or 7 as part of their number, nor are multiples of 3, 5 or 7.

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 4th & 6th rows contain the following fourteen numbers:

3   5   10   12   18   20   32   33   35   44   49   54   56   60

What is the sum of the multiples of 11?

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 FIVE ways of making 58 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 16 and once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

5    10    15    20    25    30    35    40    45    50

#5TimesTable

The Target Challenge

Can you arrive at 58 by inserting 4, 6, 8 and 10 into the gaps on each line?

•  ◯×◯–◯÷◯ = 58
•  ◯²+◯+◯+ = 58
•  ◯²–√(◯×(◯–◯)) = 58