T he Main Challenge
Group the following numbers into three groups of three so that the sum of each of the triples are the same. What is this sum?
11 25 35 43 51 63 73 85 91
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 & 7th rows of the playing board contain the following fourteen numbers:
4 6 7 11 16 21 24 27 30 50 70 77 81 84
How many square numbers are listed?
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 FIVE ways of making 140 when using Lagrange’s Theorem. Can you find them?
The Mathematically Possible Challenge
Using 3, 6 and 10 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?
50 51 52 53 54 55 56 57 58 59
#NumbersIn50s
The Target Challenge
Can you arrive at 140 by inserting 2, 6, 8 and 10 into the gaps on each line?
- ◯²+◯²+◯÷◯ = 140
- (◯+◯)²–(◯–◯)² = 140
- ◯³+◯²–◯×◯ = 140
Answers can be found here.
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