# DAY/DYDD 67: The Main Challenge

Can you correctly place 0 1 1 2 2 3 4 5 5 8 9 and 9 into the 12 gaps below?

◯  +  ◯   =    3    =   ◯  –  ◯
◯  +  ◯   =    8    =   ◯  ×  ◯
◯  +  ◯   =    1    =   ◯  ÷  ◯

Click Mathelona for details on how to purchase our number puzzle pocket book. 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 3rd & 5th rows contain the following fourteen numbers:

6   7   13   16   21   25   36   42   45   50   66   80   81   84

Which two numbers have a difference of 25? 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 FOUR ways of making 67 when using Lagrange’s Theorem. Can you find them all? The Mathematically Possible Challenge

Using 46 and 12 once each, with + – × ÷ available, which FOUR numbers is it 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 67 by inserting 4, 5, 7 and 8 into the gaps on each line?

•  ◯×◯+× = 67
•  ◯²+◯+◯×√ = 67
•  ◯³+(◯+◯)÷◯ = 67   