DAY/DYDD 108:

T he Main Challenge

Here’s seven more mental arithmetic questions to try.  Can you get all seven correct?

1.  (11 – 5) – (4 + 1) = ?
2.  What is 10 more than –4?
3.  47 × 4 = ?
4.  0.32 ÷ 4 = ?
5.  3/4 × 2/3 = ?
6.  Which one is bigger: 2 cubed or 3 squared?
7.  You wish to buy two £30 items. Which offer would give you the best deal: (A) 15% off both items, (B) 2nd item is 40% off, (C) get 1/3 off the 2nd item, (D) 25% off 1st item, 10% off 2nd item.

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

From the list, find TWO numbers that have a sum of 111.

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 SEVEN ways of making 108 when using Lagrange’s Theorem. Can you find them all?

Can you arrive at 108 by inserting 2, 3, 5 and 11 into the gaps on both lines?

•  ◯²×◯²+◯–◯ = 108
•  ◯×◯²+◯²+◯ = 108

Answers can be found here.

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