# day/dydd 105 at 7puzzleblog.com T he Main Challenge

How quickly can you correctly answer the following seven questions?

1.  (17 – 4) + (12 – 9) = ?
2.  (3 – 2) – (16 – 16) = ?
3.  What is two-thirds plus three-quarters?
4.  109 + 10 = ?
5.  (3 + 16) + (16 + 9) = ?
6.  (11 – 5) + (4 + 1) = ?
7.  What is the perimeter of a 13cm by 13cm square? 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

Which two numbers in the list are cube 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 SIX ways of making 105 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 14 and 9 once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

3    6    9    12    15    18    21    24    27    30

#3TimesTable

The Target Challenge

Can you arrive at 105 by inserting 5, 5, 6 and 10 into the gaps on both lines?

•  ◯×(◯+◯)–◯ = 105
•  ◯²+◯–◯÷◯ = 105   