# day/dydd 182 at 7puzzleblog.com T he Main Challenge

Can you place the 12 digits 0 1 1 2 3 4 5 5 6 7 9 and 9 into the gaps below so that all three lines work out arithmetically?

◯  +  ◯    =     4     =   ◯  –  ◯
◯  +  ◯    =    18    =   ◯  ×  ◯
◯  +  ◯    =     7     =   ◯  ÷  ◯

To order a pocket book full of these popular number puzzles, click 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 4th & 7th rows contain the following fourteen numbers:

3   4   10   11   24   27   30   32   35   44   54   60   70   77

Which two numbers, when each is doubled, become cube numbers? 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 182, in TEN different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 36 and 12 once each, with + – × ÷ available, which THREE target numbers is it possible to make from the list below?

10    20    30    40    50    60    70    80    90    100

#10TimesTable The Target Challenge

Can you arrive at 182 by inserting 2, 6, 7 and 14 into the gaps on each line?

•  (◯×◯+◯)×◯ = 182   (2 different ways!)
•  (◯+◯)×◯×half◯ = 182   