T he Main Challenge
Can you make all four lines work out arithmetically by placing the digits 0-9 into the 16 gaps in our latest Mathelona challenge?
◯ + ◯ = 10 = ◯ + ◯
◯ + ◯ = 1 = ◯ – ◯
◯ + ◯ = 15 = ◯ × ◯
◯ + ◯ = 5 = ◯ ÷ ◯
Note that each digit can only be inserted a maximum of TWICE.
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 1st & 5th rows contain the following fourteen numbers:
2 6 7 9 14 15 16 21 22 40 50 72 81 84
Which FOUR different numbers have a sum of 100?
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 156, in SIX different ways, when using Lagrange’s Theorem.
The Mathematically Possible Challenge
Using the three digits 3, 5 and 8 once each, with + – × ÷ available, which is the ONLY number it’s possible to make from the list below?
7 14 21 28 35 42 49 56 63 70
#7TimesTable
The Target Challenge
Can you arrive at 156 by inserting 2, 3, 5 and 7 into the gaps in each line below?
- ◯²×◯+(◯–◯)² = 156
- (◯²+◯²)×(◯+◯) = 156
- (◯+◯)²+double(◯×◯) = 156
Answers can be found here.
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