T he Main Challenge
You have been given the task of manually numbering a 100-page document from 1 to 100.
Which digit will appear most, and how many times?
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 of the playing board contain the following fourteen numbers:
2 8 9 14 15 17 22 28 40 48 55 63 64 72
What is the difference between the highest and lowest square 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 TEN different ways to make 213 when using Lagrange’s Theorem. How many can you find?
The Mathematically Possible Challenge
Using 4, 6 and 9 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?
4 8 12 16 20 24 28 32 36 40
#4TimesTable
The Target Challenge
Can you arrive at 213 by inserting 3, 4, 5 and 15 into the gaps on each line?
- (◯×◯–◯)×◯ = 213
- ◯²–(◯+◯+◯) = 213
- (◯+double◯)×◯+◯ = 213
Answers can be found here.
Click Paul Godding for details of online maths tuition.
