# day/dydd 107 at 7puzzleblog.com

T he Main Challenge

Here’s seven tricky mental teasers to try:

1.  (18 – 5) – (7 – 17) = ?
2.  128 + 294 = ?
3.  How many seconds are in a quarter-of-an-hour?
4.  How many degrees are in three-quarters of a circle?
5.  (16 – 8) × (13 – 8) = ?
6.  On four consecutive days, you spend £55, £74, £36 and £15. What is the average amount spent per day?
7.  What is 15% of £8?

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 & 2nd rows contain the following fourteen numbers:

2   8   9   14   15   17   22   28   40   48   55   63   64   72

Which two numbers have a difference of 42?

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 FOUR ways of making 107 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 14 and once each, with + – × ÷ available, which FOUR numbers is it 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 107 by inserting 9, 10, 11 and 12 into the gaps on both lines?

•  ◯×◯+◯–◯ = 107   (2 different ways!)
•  ◯×◯+(◯–◯)³ = 107