T he Main Challenge
From all the odd numbers in the range 1-23 inclusive, eliminate all prime numbers and multiples of 3. Which is the only number that remains?
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 3rd & 4th rows of the playing board contain the following fourteen numbers:
3 10 13 25 32 35 36 42 44 45 54 60 66 80
Which number, when 10 is added to it, becomes a square number?
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 ELEVEN different ways to make 218 when using Lagrange’s Theorem. How many can you find?
The Mathematically Possible Challenge
Using 4, 6 and 9 once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?
11 22 33 44 55 66 77 88 99 110
#11TimesTable
The Target Challenge
Can you arrive at 218 by inserting 4, 10, 12 and 17 into the gaps on each line?
- ◯×◯+◯+◯ = 218
- ◯×◯+◯×◯ = 218
- ◯²–◯×(◯–◯)+1 = 218
- ◯×(◯+◯)+treble◯–1 = 218
Answers can be found here.
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