T he Main Challenge
From the numbers in the range 1-50, eliminate the following:
- multiples of 3
- square numbers
- prime numbers
- even numbers
Which number is the only one 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 6th & 7th rows of the playing board contain the following fourteen numbers:
4 5 11 12 18 20 24 27 30 33 49 56 70 77
Which number, when 20 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 SEVEN different ways to make 199 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?
4 8 12 16 20 24 28 32 36 40
#4TimesTable
The Target Challenge
Can you arrive at 199 by inserting 11, 12, 14 and 20 into the gaps on each line?
- ◯×◯+◯+◯ = 199
- ◯²+◯+◯–◯ = 199
Answers can be found here.
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