# day/dydd 12 at 7puzzleblog.com

The Main Challenge

Add together the 7th prime number, the 7th square number, the 7th 2-digit number and the 7th whole number that contains a 7. What is your answer?

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 5th & 6th rows contain the following fourteen numbers:

5   6   7   12   16   18   20   21   33   49   50   56   81   84

Which two numbers listed have a sum of 101?

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 TWO ways to make 12 when using Lagrange’s Theorem. Can you find both?

The Mathematically Possible Challenge

Using 45 and 10 once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

40    41    42    43    44    45    46    47    48    49

#NumbersIn40s

The Target Challenge

Can you arrive at 12 by inserting 2, 3, 4 and 6 into the gaps on each line?

•  (◯–◯)×◯×◯ = 12
•  ◯×◯(◯+◯) = 12
•  ◯÷◯×(◯+◯) = 12
•  ◯²–◯×◯÷◯ = 12
•  (◯²+◯³)×◯÷◯ = 12