Th e Main Challenge
From the following list of eighteen numbers, eliminate all square numbers, multiples of 8, factors of 60 and prime numbers.
3 4 7 10 11 15 16 17 24 27 30 32 36 48 49 54 56 64
What is the sum of the TWO numbers that remain?
The 7puzzle Challenge
The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from 2 up to 84.
The 3rd & 7th rows contain the following fourteen numbers:
4 11 13 24 25 27 30 36 42 45 66 70 77 80
How many even numbers, when halved, become odd numbers?
The Lagrange Challenge
Lagrange’s Four-Square Theorem states that every integer can be made by adding up to four square numbers.
For example, 7 can be made by 2²+1²+1²+1² (4+1+1+1).
Show how you can make 154, in TEN different ways, when using Lagrange’s Theorem.
The Mathematically Possible Challenge
Using the three digits 3, 5 and 8 once each, with + – × ÷ available, which are the only TWO numbers it’s possible to make from the list below?
5 10 15 20 25 30 35 40 45 50
#5TimesTable
The Target Challenge
Can you arrive at 154 by inserting 5, 6, 7 and 8 into the gaps in each line below?
- (◯×◯–◯)×◯ = 154
- ◯²+◯²+◯²+◯ = 154
Answers can be found here.
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