# day/dydd 221 at 7puzzleblog.com

T he Main Challenge

Group the following numbers into three lots of three so the products of each of the triples are the same. What is this product?

3     4     5     6     7     8     28     30     35

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

From the list, which pair of numbers have a sum of 77?

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

The Mathematically Possible Challenge

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

2    3    5    7    11    13    17    19    23    29

The Target Challenge

Can you arrive at 221 by inserting 567 and 10 into the gaps on each line?

•  (◯+◯)²–◯×◯ = 221
•  (◯+◯+1)×(◯+◯+1) = 221

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