# day/dydd 213 at 7puzzleblog.com

T he Main Challenge

You have been given the task of manually numbering a 100-page document from 1 to 100.

Which digit will appear most, and how many times?

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 of the playing board contain the following fourteen numbers:

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

What is the difference between the highest and lowest square numbers?

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 TEN different ways to make 213 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Using 46 and once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

4    8    12    16    20    24    28    32    36    40

#4TimesTable

The Target Challenge

Can you arrive at 213 by inserting 345 and 15 into the gaps on each line?

•  (◯×◯–◯)×◯ = 213
•  ◯²–(◯+◯+◯) = 213
•  (◯+double◯)×◯+◯ = 213