# day/dydd 88 at 7puzzleblog.com

T he Main Challenge

In our latest Mathelona challenge, can you place the 12 listed numbers into the 12 gaps so all three lines work out arithmetically?

0    1    1    2    2    3    4    5    6    7    8    9

◯  +  ◯   =     1     =   ◯  –  ◯
◯  +  ◯   =    12    =   ◯  ×  ◯
◯  +  ◯   =     3     =   ◯  ÷  ◯

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 2 up to 84.

The 4th & 5th rows contain the following fourteen numbers:

3   6   7   10   16   21   32   35   44   50   54   60   81   84

Which two different numbers 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 just TWO ways of making 88 when using Lagrange’s Theorem. Can you find them both?

The Mathematically Possible Challenge

Using 23 and 11 once each, with + – × ÷ available, which SIX numbers is it possible to make from the list below?

2    3    5    7    11    13    17    19    23    29

The Target Challenge

Can you arrive at 88 by inserting 1, 4, 8 and 10 into the gaps on each line?

•  ²–◯×(◯+◯) = 88
•  (◯+◯)×◯–√◯ = 88
•  (◯+◯)×◯×³ = 88