T he Main Challenge
As an example, both 4 and 8 can be written as the sum of two prime numbers, as shown here:
- 4 = 2+2
- 8 = 5+3
… but how many numbers less than 20 CANNOT be written as the sum of two prime numbers?
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 & 7th rows of the playing board contain the following fourteen numbers:
2 4 9 11 14 15 22 24 27 30 40 70 72 77
Which four different numbers above have a sum of 100?
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 TEN different ways to make 228 when using Lagrange’s Theorem. How many can you find?
The Mathematically Possible Challenge
Using 2, 4 and 8 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 228 by inserting 3, 4, 5 and 6 into the gaps on each line?
- ◯×(◯²+◯²–◯) = 228
- ◯×(◯²×◯+double◯) = 228
Answers can be found here.
Click Paul Godding for details of online maths tuition.
