T he Main Challenge
Three unique digits from 1-9 must be used to arrive at the target number 18 when multiplying two numbers together and adding or subtracting the third unique number, (a×b)±c.
One way of arriving at 18 is (5×4)–2. Find the other FOUR ways it is possible to make 18.
[Note: (5×4)–2 = 18 and (4×5)–2 = 18 counts as just ONE way.]
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
Which number above 20 becomes a multiple of 11 when 20 is subtracted from it?
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 169, in EIGHT different ways, when using Lagrange’s Theorem.
The Mathematically Possible Challenge
Using 4, 6 and 10 once each, with + – × ÷ available, which are the only FOUR numbers it’s possible to make from the list below?
8 16 24 32 40 48 56 64 72 80
#8TimesTable
The Target Challenge
Can you arrive at 169 by inserting 1, 3, 13 and 15 into the gaps on each line?
- ◯×(◯+◯–◯) = 169
- (◯–◯)²+(◯÷◯)² = 169
Answers can be found here.
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