# DAY 176: The Main Challenge

You have been given the task of manually numbering a 100-page document from 1 to 100. What is the total of all the individual digits written? The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from up to 84.

The 1st & 6th rows contain the following fourteen numbers:

2   5   9   12   14   15   18   20   22   33   40   49   56   72

Find three pairs of numbers that each have a sum of 42. 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 (or 4+1+1+1).

Show how you can make 176, in TWO different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 36 and 12 once each, with + – × ÷ available, which THREE target numbers is it 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 176 by inserting 6, 7, 8 and 9 into the gaps on each line?

•  (◯+◯+◯)×◯ = 176
•  ◯²+◯²+◯²–treble◯ = 176 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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