# DAY/DYDD 149: The Main Challenge

You have been given the task of manually numbering a 100-page document from 1 to 100. How many digits will you write altogether? 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 2nd & 6th rows contain the following fourteen numbers:

5   8   12   17   18   20   28   33   48   49   55   56   63   64

How many prime numbers and square numbers are listed altogether? The Lagrange 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 149, in SIX different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using the three digits 26 and 9 once each, with + – × ÷ available, which are the only TWO numbers it’s possible to make from the list below?

1    4    9    16    25    36    49    64    81    100

#SquareNumbers The Target Challenge

Can you arrive at 149 by inserting 346 and 10 into the gaps on each line?

•  ◯²+◯²+◯²+◯ = 149
•  (◯+◯)²–double(◯+◯) = 149 Answers can be found here. Click Paul Godding for details of online maths tuition. This entry was posted in 7puzzleblog.com. Bookmark the permalink.

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