# day/dydd 114 at 7puzzleblog.com

T he Main Challenge

Can you place the numbers 1 2 3 4 5 6 8 9 10 11 12 and 13 into the 12 gaps below so all four lines work out arithmetically?

◯   +   ◯   =   ◯
◯   +   ◯   =   ◯
◯   +   ◯   =   ◯
◯   +   ◯   =   ◯

Click this Mathelona link for details of similar challenges.

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 3rd & 4th rows contain the following fourteen numbers:

3   10   13   25   32   35   36   42   44   45   54   60   66   80

List THREE different numbers that have a sum of 100.

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 EIGHT ways of making 114 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

Using 14 and once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

30    31    32    33    34    35    36    37    38    39

#NumbersIn30s

The Target Challenge

Can you arrive at 114 by inserting 3, 6, 12 and 16 into the gaps on both lines?

•  (◯+◯)×(◯–◯) = 114
•  ◯²–◯×(◯–◯) = 114

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.