DAY/DYDD 104:

The Main Challenge

Here’s another selection of mental arithmetic questions.  Can you answer all seven correctly?

1.  (10 + 10) – (15 – 3) = ?
2.  What is the sum of 0.83 and 0.89?
3.  What is 1 × 9?
4.  If Ben earns £10 every half-hour, how much will he earn in 40 hours?
5.  If you burn 100 calories by climbing 100 stairs, how many calories would you burn when climbing 50 stairs?
6.  What is 5,456 – 4,372?
7.  Twice my age plus 4 more is 72. How old am I?

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

What is the product of the two prime 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 just THREE ways of making 104 when using Lagrange’s Theorem. Can you find them?

Can you arrive at 104 by inserting 2, 4, 12 and 15 into the gaps on both lines?

•  (◯–◯)×(◯–◯) = 104
•  ◯×(◯+◯)–◯² = 104

Answers can be found here.

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