T he Main Challenge
Here’s a mini-Mathelona challenge where you must place the eight digits 0 1 1 2 2 2 3 and 4 into the eight gaps so both lines work out arithmetically:
◯ + ◯ = 4 = ◯ × ◯
◯ – ◯ = 2 = ◯ ÷ ◯
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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 & 6th rows contain the following fourteen numbers:
3 5 10 12 18 20 32 33 35 44 49 54 56 60
Which two numbers, when each is divided by 6, also appear on the list?
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 162, in THIRTEEN different ways, when using Lagrange’s Theorem.
The Mathematically Possible Challenge
Using the three digits 3, 5 and 8 once each, with + – × ÷ available, which TWO numbers is it possible to make from the list below?
1 8 27 64 125
#CubeNumbers
The Target Challenge
Can you arrive at 162 by inserting 2, 3, 9 and 12 into the gaps on each line?
- ◯×◯×(◯–◯) = 162
- ◯³×(◯×◯–◯) = 162
Answers can be found here.
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