# DAY/DYDD/PÄIVÄ/NAP 110 at 7puzzleblog.com T he Main Challenge

Carry out these instructions in our 7-step challenge:

1.  Work out the sum of 4 and 6,
2.  Calculate the product of 4 and 6,
3.  Find the difference between the two answers in Points 1 and 2,
4.  Square the answer to Point 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 1st & 2nd rows contain the following fourteen numbers:

2   8   9   14   15   17   22   28   40   48   55   63   64   72

What is the product of the smallest and largest numbers on this list? 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 SIX ways of making 110 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 14 and once each, with + – × ÷ available, which TWO numbers is it 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 110 by inserting 6, 7, 8 and 10 into the gaps on both lines?

•  (◯+◯)×◯+◯ = 110
•  (◯+◯)×◯+double◯ = 110   