# DAY/DYDD/GIORNO/NAP 140: T he Main Challenge

Group the following numbers into three groups of three so that the sum of each of the triples are the same. What is this sum?

11    25    35    43    51    63    73    85    91 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 & 7th rows of the playing board contain the following fourteen numbers:

4   6   7   11   16   21   24   27   30   50   70   77   81   84

How many square numbers are listed? 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 FIVE ways of making 140 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 36 and 10 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

50    51    52    53    54    55    56    57    58    59

#NumbersIn50s

The Target Challenge

Can you arrive at 140 by inserting 2, 6, 8 and 10 into the gaps on each line?

•  ◯²+◯²+◯÷◯ = 140
•  (◯+◯)²–(◯–◯)² = 140
•  ◯³+◯²–◯×◯ = 140   