T he Main Challenge
Using each of the numbers 0.5, 1, 1.5 and 2 once each, with the four arithmetical operations + – × ÷ available, can you arrive at the target answer of 7?
For the number puzzle enthusiast, can you find a 2nd way of making 7?
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 2nd & 5th rows contain the following fourteen numbers:
6 7 8 16 17 21 28 48 50 55 63 64 81 84
Which THREE numbers, when 19 is added to each of them, become 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 FIVE ways of making 101 when using Lagrange’s Theorem. Can you find them all?
The Mathematically Possible Challenge
Using 5, 7 and 10 once each, with + – × ÷ available, which TWO numbers 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 101 by inserting 5, 8, 10 and 11 into the gaps on each line?
- ◯×◯–(◯–◯)² = 101
- (◯+◯)×◯+◯ = 101
- ◯×◯+◯+double◯ = 101
Answers can be found here.
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