T he Main Challenge
We invite you to use seven 3’s (3 3 3 3 3 3 and 3) once each, with + – × ÷ available, to make various target numbers.
For instance, to make 1 and 2, you could do:
- 3 × (3÷3) – (3÷3) – (3÷3) = 1
- (3+3) × (3÷3) × (3÷3) ÷ 3 = 2 . . . and so on.
Continuing, as above, can you make the target numbers from 3 to 6?
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
Find three different numbers from the list that have a sum of 100.
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 THIRTEEN different ways to make 243 when using Lagrange’s Theorem. How many of them can you find?
The Mathematically Possible Challenge
Using 2, 5 and 10 once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?
12 24 36 48 60 72 84 96 108 120
#12TimesTable
The Target Challenge
Can you arrive at 243 by inserting 2, 3, 4, 5 and 6 into the gaps below?
- ◯×(◯+◯)²+(◯+◯)² = 243
Answers can be found here.
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