# DAY 145:

The Main Challenge

Lagrange’s Four-Square Theorem states that every integer can be made by adding up to four square numbers.

For example, 7 can be made by 2²+1²+1²+1² (4+1+1+1).

Show how you can make 31 when using Lagrange’s Theorem in TWO different ways.

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 1st & 4th rows of the playing board contain the following fourteen numbers:

2   3   9   10   14   15   22   32   35   40   44   54   60   72

What is the sum of the multiples of 5?

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using the three digits 2, 6 and 9 once each, with + – × ÷ available, which are the only THREE numbers it’s 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 145 by inserting 3, 4, 5 and 8 into the gaps on each line?

•  (◯×◯–◯)×◯ = 145
•  (◯+◯)²–double(◯×◯) = 145
•  (◯+◯)²+half(◯–◯) = 145

Answers can be found here.

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