# day/dydd 17 at 7puzzleblog.com The Main Challenge

Find the answer to this large number trail which involves fourteen arithmetical steps and includes fraction and percentage calculations.

• double it
• 50% of this
• +50
• subtract thirty-five
• ÷2
• +37
• 3/5 of this
• +70
• 2%
• 1/2 of this
• +311
• subtract twenty
• ÷7 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 1st & 7th rows contain the following fourteen numbers:

2   4   9   11   14   15   22   24   27   30   40   70   72   77

What is the difference between the highest multiples of 5 and 6? 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 only TWO ways of making 17 when using Lagrange’s Theorem. Can you find both? The Mathematically Possible Challenge

Using 56 and once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

7    14    21    28    35    42    49    56    63    70

#7TimesTable

The Target Challenge

Can you arrive at 17 by inserting 2, 5, 6 and 6 into the gaps on each line?

•  ◯²–√(◯×◯)–◯ = 17
•  ◯²×◯÷◯+◯ = 17
•  (◯÷◯+◯)×◯ = 17   