T he Main Challenge
Can you place the 12 digits 0 1 1 2 3 4 5 5 6 7 9 and 9 into the gaps below so that all three lines work out arithmetically?
◯ + ◯ = 4 = ◯ – ◯
◯ + ◯ = 18 = ◯ × ◯
◯ + ◯ = 7 = ◯ ÷ ◯
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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 4th & 7th rows contain the following fourteen numbers:
3 4 10 11 24 27 30 32 35 44 54 60 70 77
Which two numbers, when each is doubled, become cube 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 (or 4+1+1+1).
Show how you can make 182, in TEN different ways, when using Lagrange’s Theorem.
The Mathematically Possible Challenge
Using 3, 6 and 12 once each, with + – × ÷ available, which THREE target numbers is it possible to make from the list below?
10 20 30 40 50 60 70 80 90 100
#10TimesTable
The Target Challenge
Can you arrive at 182 by inserting 2, 6, 7 and 14 into the gaps on each line?
- (◯×◯+◯)×◯ = 182 (2 different ways!)
- (◯+◯)×◯×half◯ = 182
Answers can be found here.
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