T he Main Challenge
There is just one set of three consecutive numbers in ascending order whose sum is less than 50 and follow this sequence:
- prime number – cube number – square number
What is the sum of these three 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 6th & 7th rows of the playing board contain the following fourteen numbers:
4 5 11 12 18 20 24 27 30 33 49 56 70 77
What is the sum of the multiples of 11?
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).
Show how you can make 197, in SEVEN different ways, when using Lagrange’s Theorem.
The Mathematically Possible Challenge
Using 3, 4 and 12 once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?
2 3 5 7 11 13 17 19 23 29
#PrimeNumbers
The Target Challenge
Can you arrive at 197 by inserting 1, 4, 11 and 14 into the gaps on each line?
- ◯×(◯+◯)–◯ = 197
- (◯+◯)²–(◯×double◯) = 197
Answers can be found here.
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