# day/dydd 158 at 7puzzleblog.com T he Main Challenge

Here’s a 10-step number trail involving all four arithmetical operations together with the numbers 1, 2 and 3.

Starting with 10, carry out the following steps:

• ×1
• ÷3
• 2
• multiply by 3
• +1
• subtract 3
• divide by 1
• ×2
• take away two 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

Find two separate pairs of numbers that each have a difference of 44. 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 (4+1+1+1).

Show how you can make 158, in SIX different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using the three digits 35 and 8 once each, with + – × ÷ available, which is the ONLY number it’s possible to make from the list below?

9    18    27    36    45    54    63    72    81    90

#9TimesTable The Target Challenge

Can you arrive at 158 by inserting 7810 and 11 into the gaps below?

•  ◯×◯+◯×◯ = 158   