# DAY/DYDD 114: T he Main Challenge

Can you place the numbers 1 2 3 4 5 6 8 9 10 11 12 and 13 into the 12 gaps below so all four lines work out arithmetically?

◯   +   ◯   =   ◯
◯   +   ◯   =   ◯
◯   +   ◯   =   ◯
◯   +   ◯   =   ◯

Click this Mathelona link for details of similar challenges. The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from up to 84.

The 3rd & 4th rows contain the following fourteen numbers:

3   10   13   25   32   35   36   42   44   45   54   60   66   80

List THREE different numbers that have a sum of 100. 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 EIGHT ways of making 114 when using Lagrange’s Theorem. Can you find them all? The Mathematically Possible Challenge

Using 14 and once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

30    31    32    33    34    35    36    37    38    39

#NumbersIn30s

The Target Challenge

Can you arrive at 114 by inserting 3, 6, 12 and 16 into the gaps on both lines?

•  (◯+◯)×(◯–◯) = 114
•  ◯²–◯×(◯–◯) = 114   