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 2 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?

Can you arrive at 107 by inserting 9, 10, 11 and 12 into the gaps on both lines?

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

Answers can be found here.

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