# day/dydd 238 at 7puzzleblog.com T he Main Challenge

Here’s a 12-step number trail involving + – × ÷ and the numbers 4 and 5.

• +5
• ÷5
• multiply by 4
• subtract 4
• ×5
• divide by 5
• 5
• ÷4
• +4
• ÷5 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 3rd & 6th rows of the playing board contain the following fourteen numbers:

5   12   13   18   20   25   33   36   42   45   49   56   66   80

How many square numbers are listed above? 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 TEN different ways to make 238 when using Lagrange’s Theorem. How many of them can you find? The Mathematically Possible Challenge

Using 25 and 10 once each, with + – × ÷ available, which are the SIX numbers it is possible to make from the list below?

5    10    15    20    25    30    35    40    45    50

#5TimesTable The Target Challenge

Can you arrive at 238 by inserting 5678 and 9 into the gaps below?

•  ◯×◯×◯+◯–◯ = 238   