T he Main Challenge
Group the following numbers into three lots of three so the products of each of the triples are the same. What is this product?
3 4 5 6 7 8 28 30 35
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 5th & 6th rows of the playing board contain the following fourteen numbers:
5 6 7 12 16 18 20 21 33 49 50 56 81 84
From the list, which pair of numbers have a sum of 77?
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 221 when using Lagrange’s Theorem. How many can you find?
The Mathematically Possible Challenge
Using 4, 6 and 9 once each, with + – × ÷ available, which are the only THREE numbers it is 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 221 by inserting 5, 6, 7 and 10 into the gaps on each line?
- (◯+◯)²–◯×◯ = 221
- (◯+◯+1)×(◯+◯+1) = 221
Answers can be found here.
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