T he Main Challenge
This puzzle invites you to use seven 2’s (2 2 2 2 2 2 and 2), with + – × ÷ available, in each separate calculation.
For instance, to make 1 and 2 you could simply do:
- 2 + (2÷2) – (2÷2) – (2÷2) = 1
- 2 + 2 + 2 + 2 – 2 – 2 – 2 = 2
Can you show how to make 3, 4, and 5 when using seven 2’s?
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 of the playing board contain the following fourteen numbers:
6 7 8 16 17 21 28 48 50 55 63 64 81 84
Which four numbers, when 2 is added to them, each become multiples of 5?
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 different ways to make 208 when using Lagrange’s Theorem. How many can you find?
The Mathematically Possible Challenge
Using 5, 7 and 11 once each, with + – × ÷ available, which are the only 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 208 by inserting 4, 5, 6 and 8 into the gaps on each line?
- (◯×◯+◯)×◯ = 208
- (◯×◯–◯)×◯ = 208
- ◯³–◯×(◯–◯) = 208
- (◯+◯)×(◯+double◯) = 208
Answers can be found here.
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