# day/dydd 102 at 7puzzleblog.com T he Main Challenge

Can you place the 16 numbers 0 0 1 1 2 2 3 4 4 5 6 7 7 8 9 9 into the 16 gaps below so all four lines work out arithmetically?

◯  +  ◯   =     9     =   ◯  +  ◯
◯  +  ◯   =     7     =   ◯  –  ◯
◯  +  ◯   =    12    =   ◯  ×  ◯
◯  +  ◯   =     6     =   ◯  ÷  ◯

If you enjoyed this number puzzle, click Mathelona 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 2 up to 84.

The 2nd & 5th rows contain the following fourteen numbers:

6   7   8   16   17   21   28   48   50   55   63   64   81   84

What is the sum of the square numbers? 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 SEVEN ways of making 102 when using Lagrange’s Theorem. Can you find them all? The Mathematically Possible Challenge

Using 57 and 10 once each, with + – × ÷ available, which is the ONLY number 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 102 by inserting 3, 4, 6 and 10 into the gaps on both lines?

•  (+◯+◯)×◯ = 102
•  ◯²+◯×◯÷ = 102   