# day/dydd 165 at 7puzzleblog.com T he Main Challenge

Which THREE different prime numbers have a sum of 40? 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 factors of 120? 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 165, in EIGHT different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

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

4    8    12    16    20    24    28    32    36    40

#4TimesTable The Target Challenge

Can you arrive at 165 by inserting 5, 10, 15 and 20 into the gaps on each line?

•  (◯+◯)×◯+◯ = 165
•  (◯+◯)×◯–◯ = 165   