day/dydd 184 at 7puzzleblog.com T he Main Challenge

Read the following clues to work out which number I am today:

•  I am a 2-digit number,
•  Both 3 and 4 divide exactly into me,
•  My two digits add up to 9,
•  I am not a square number.

Who am I? 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 even number, when halved, becomes a square number? 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 184, in TWO different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

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

1    4    9    16    25    36    49    64    81    100

#SquareNumbers The Target Challenge

Can you arrive at 184 by inserting 456 and 8 into the gaps on each line?

•  (◯×◯+◯)×◯ = 184
•  (◯×◯+half◯)×◯ = 184   