T he Main Challenge
Of the numbers 1, 2, 3 . . . 6000, how many are NOT multiples of 2, 3 or 5?
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 4th & 5th rows contain the following fourteen numbers:
3 6 7 10 16 21 32 35 44 50 54 60 81 84
What is the average of the two prime numbers on the list?
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 89 when using Lagrange’s Theorem. Can you find them?
The Mathematically Possible Challenge
Using 2, 3 and 11 once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?
30 31 32 33 34 35 36 37 38 39
#NumbersIn30s
The Target Challenge
Can you arrive at 89 by inserting 1, 4, 8 and 10 into the gaps on each line?
- ◯²+◯²+◯–◯ = 89
- ◯×◯+(◯–◯)² = 89
- (◯+◯)³–double(◯+◯) = 89
Answers can be found here.
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