# day/dydd 222 at 7puzzleblog.com

T he Main Challenge

You’ve rolled the numbers 1, 3 and 3 with three dice.  Using these once each, with + – × ÷ available, find the TWO target numbers from 1-10 that it is NOT possible to make.

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

What is the sum of the multiples of 5 on the 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 ELEVEN different ways to make 222 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    4    6    8    10    12    14    16    18    20

#EvenNumbers

The Target Challenge

Can you arrive at 222 by inserting 356 and 8 into the gaps on each line?

•  (◯×◯–◯)×◯ = 222
•  ◯³+◯+◯–◯ = 222

Answers can be found here.

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