day/dydd 109 at 7puzzleblog.com

T he Main Challenge

Last chance to get all seven correct. Be careful as there may be one or two tricky ones!

1.  (1 – 2) – (3 – 4) = ?
2.  4 ÷ 0.5 = ?
3.  What is 25 less than the product of 20 and 10?
4.  How do you write “Six and six hundredths” in decimal format?
5.  4,000 × 0.02 = ?
6.  Find 10% of £13.
7.  What is 31 × 15?

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

What is the sum of the odd 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 FIVE ways of making 109 when using Lagrange’s Theorem. Can you find them?

Can you arrive at 109 by inserting 3, 8, 10 and 12 into the gaps on both lines?

•  ◯×◯–(◯+◯) = 109
•  ◯×◯+◯+◯ = 109

Answers can be found here.

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