# DAY/DYDD/GIORNO/NAP 223: T he Main Challenge

Try the following challenge from my number puzzle pocket book.  Further details can be found by clicking on Mathelona.

Your task is to make all three lines work out arithmetically by correctly placing the 12 digits 0 0 1 1 2 2 3 3 4 4 6 and 6 into the 12 gaps below. Can you do it?

◯  +  ◯   =    4    =   ◯  –  ◯
◯  +  ◯   =    6    =   ◯  ×  ◯
◯  +  ◯   =    3    =   ◯  ÷  ◯ 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 5th & 6th rows of the playing board contain the following fourteen numbers:

5   6   7   12   16   18   20   21   33   49   50   56   81   84

What is the answer when the larger multiple of 10 is divided by the smaller one? 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 NINE different ways to make 223 when using Lagrange’s Theorem. How many can you find? The Mathematically Possible Challenge

Using 46 and once each, with + – × ÷ available, which are the FIVE numbers it is possible to make from the list below?

1    3    5    7    9    11    13    15    17    19

#OddNumbers The Target Challenge

Can you arrive at 223 by inserting 378 and 20 into the gaps on each line?

•  ◯²×◯+◯×◯ = 223
•  (◯⁵–◯)÷(◯–◯) = 223   