# DAY/DYDD/GIORNO/NAP 231:

T he Main Challenge

Try the following Mathelona-style challenge, similar to those found in our pocket book of number puzzles.

0    0    1    2    2    2    2    4    4    5    5    6    6    7    7    8

◯  +  ◯   =     6     =   ◯  +  ◯
◯  +  ◯   =     5     =   ◯  –  ◯
◯  +  ◯   =    12    =   ◯  ×  ◯
◯  +  ◯   =     7     =   ◯  ÷  ◯

Your task is to make all four lines work out arithmetically by placing the 16 listed digits into the 16 gaps.  Can you complete it?

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 2nd & 4th rows of the playing board contain the following fourteen numbers:

3   8   10   17   28   32   35   44   48   54   55   60   63   64

From the list, find two pairs of numbers that each have a difference of 29.

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 231 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Using 24 and once each, with + – × ÷ available, which are the SIX numbers it is possible to make from the list below?

8    16    24    32    40    48    56    64    72    80

#8TimesTable

The Target Challenge

Can you arrive at 231 by inserting 510, 1520 and 25 into the gaps below?

•  ◯×◯–◯–◯÷◯ = 231