# day/dydd 56 at 7puzzleblog.com T he Main Challenge

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

◯  +  ◯   =     6     =   ◯  –  ◯
◯  +  ◯   =    18    =   ◯  ×  ◯
◯  +  ◯    =    3     =   ◯  ÷  ◯

If you enjoyed trying this puzzle, visit our Mathelona page for further details. 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

How many triangular numbers are listed above? 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 is only ONE way of making 56 when using Lagrange’s Theorem. Can you find it? The Mathematically Possible Challenge

Using 16 and once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

3    6    9    12    15    18    21    24    27    30

#3TimesTable

The Target Challenge

Can you arrive at 56 by inserting 2, 4, 6 and 8 into the gaps on each line?

•  ◯×◯+◯×◯ = 56
•  ◯²+×◯+ = 56
•  (◯+)×◯–◯ = 56
•  (◯+)×◯–◯⁴ = 56
•  ◯×(◯+◯÷◯) = 56
•  (◯+◯)×(◯–◯)² = 56   