# DAY/DYDD/PÄIVÄ/NAP 57

T he Main Challenge

Place the 12 numbers 1 1 2 2 3 3 4 4 5 6 7 and 8 into the 12 gaps below so all three lines work out:

◯  +  ◯   =    5    =   ◯  –  ◯
◯  +  ◯   =    9    =   ◯  ×  ◯
◯  +  ◯   =    8    =   ◯  ÷  ◯

Can you complete this Mathelona challenge?

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

Which four different numbers from the list 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 FOUR ways of making 57 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 16 and once each, with + – × ÷ available, which TWO 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 57 by inserting 3, 4, 6 and 11 into the gaps in both lines?

•  ◯×◯+◯×◯ = 57
•  (◯+◯+√◯)× = 57