# day/dydd 183 at 7puzzleblog.com

T he Main Challenge

Simply add together the first seven positive square numbers and the first seven prime numbers. What is the total of these 14 numbers?

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 4th & 7th rows contain the following fourteen numbers:

3   4   10   11   24   27   30   32   35   44   54   60   70   77

Which three numbers become square numbers when 5 is added to them?

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 183, in SEVEN different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Using 36 and 12 once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

12    24    36    48    60    72    84    96    108    120

#12TimesTable

The Target Challenge

Can you arrive at 183 by inserting 1, 5, 8 and 14 into the gaps on each line?

•  (◯+◯)×◯+◯ = 183
•  half ((◯+◯)²+◯+half◯) = 183

Answers can be found here.

Click Paul Godding for details of online maths tuition.

This entry was posted in 7puzzleblog.com. Bookmark the permalink.

This site uses Akismet to reduce spam. Learn how your comment data is processed.