# day/dydd 167 at 7puzzleblog.com

T he Main Challenge

Find the sum of all the numbers between 5 and 25 that are divisible by 3, 4 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 2nd & 7th rows contain the following fourteen numbers:

4   8   11   17   24   27   28   30   48   55   63   64   70   77

Which number, when 4 is subtracted from it, becomes a multiple of 15?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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 167, in FIVE different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Using 46 and 10 once each, with + – × ÷ available, which are the only TWO numbers it’s possible to make from the list below?

6    12    18    24    30    36    42    48    54    60

#6TimesTable

The Target Challenge

Can you arrive at 167 by inserting 8, 9, 10 and 15 into the gaps on each line?

•  ◯×◯+◯+◯ = 167
•  ³√◯×◯²+◯–◯ = 167