# day/dydd 284 at 7puzzleblog.com

The Main Challenge

Another Mathelona challenge with a difference; no addition calculations at all.

Your task is to make all four lines work out arithmetically by filling the 16 gaps with digits from 0 to 9.  Each digit can only be inserted a maximum of TWICE:

◯  –  ◯   =    9    =   ◯  ×  ◯
◯  –  ◯   =    7    =   ◯  ÷  ◯
◯  –  ◯   =    5    =   ◯  ×  ◯
◯  –  ◯   =    3    =   ◯  ÷  ◯

Full details of our popular number puzzle can be found by clicking Mathelona.

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 1st & 6th rows contain the following fourteen numbers:

2   5   9   12   14   15   18   20   22   33   40   49   56   72

Which two numbers, when doubled, are also on the list?

The Factors Challenge

Which of the following numbers are factors of 284?

2     4     6     8     10     12     14     16

The Mathematically Possible Challenge

Using 27 and 10 once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

2    3    5    7    11    13    17    19    23    29

The Target Challenge

Can you arrive at 284 by inserting 5, 6, 8, 9 and 11 into the gaps below?

•  (◯²+◯²)×√◯–(◯+◯) = 284