T he Main Challenge
Study the seven clues and place the numbers 1-9 into the nine positions on this 3-by-3 grid. Each number should appear exactly once:
x x x
x x x
x x x
Clues:
- The 8 is directly above the 5,
- The 6 is further right than the 7,
- The 7 is further right than the 1,
- The 1 is lower than the 5,
- The 5 is further right than the 9,
- The 3 is higher than the 9 and further right than the 2,
- The 4 is higher than the 7 and further right than the 8.
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 2nd & 7th rows contain the following fourteen numbers:
4 8 11 17 24 27 28 30 48 55 63 64 70 77
What is the difference between the sum of the highest and lowest even numbers and the product of the highest and lowest even 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 170, in ELEVEN different ways, when using Lagrange’s Theorem.
The Mathematically Possible Challenge
Using 4, 6 and 10 once each, with + – × ÷ available, which is the ONLY target number it’s possible to make from the list below?
9 18 27 36 45 54 63 72 81 90
#9TimesTable
The Target Challenge
Can you arrive at 170 by inserting 9, 10, 20 and 20 into the gaps on each line?
- ◯+◯×◯–◯ = 170
- (◯–◯÷◯)×◯ = 170
Answers can be found here.
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