# day/dydd 53 at 7puzzleblog.com T he Main Challenge

From the numbers below, eliminate all:

• square numbers,
• triangular numbers,
• multiples of 4 and
• factors of 70.

1  2  3  4  5  6  7  8  9  10  12  14  15  16  18  20  21  24  25

Which is the only number left remaining? 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 1st & 5th rows contain the following fourteen numbers:

2   6   7   9   14   15   16   21   22   40   50   72   81   84

What is the difference between the lowest and highest multiples of 5? 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 THREE ways of making 53 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 89 and 10 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

70    71    72    73    74    75    76    77    78    79

#NumbersIn70s

The Target Challenge

Can you arrive at 53 by inserting 4, 4, 5 and 6 into the gaps on each line?

•  (◯+◯)×◯+◯ = 53
•  ◯²+◯×◯+◯ = 53
•  ◯²×◯–(◯+◯) = 53   