T he Main Challenge
The ten letters, A-J, in the following two sections each contains a calculation. Which is the only letter that has the same answer in both sections?
- Section 1
E:6÷6 I:5+1 G:3+2 A:10–2 J:4+3 C:5×1 F:6÷3 B:8–4 H:9÷3 D:4×2
- Section 2
H:4–3 A:6÷1 I:3×3 B:6–1 F:6–4 J:8÷2 E:5×2 G:4×1 D:9–3 C:2+1
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 3rd & 4th rows of the playing board contain the following fourteen numbers:
3 10 13 25 32 35 36 42 44 45 54 60 66 80
What is the difference between the two largest 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 NINE different ways to make 220 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?
1 4 9 16 25 36 49 64 81 100
#SquareNumbers
The Target Challenge
Can you arrive at 220 by inserting 5, 10, 20 and 30 into the gaps on each line?
- (◯+◯)×◯+◯ = 220
- (◯+◯)×◯–◯ = 220
- ◯×◯+◯–double◯ = 220
- (◯+◯)²–half(◯–◯) = 220
- ◯×(◯÷◯)³–◯ = 220
Answers can be found here.
Click Paul Godding for details of online maths tuition.
