T he Main Challenge
Solve all four lines arithmetically by filling the 16 gaps below with digits 0-9, but each digit must only be inserted a maximum of TWICE in the whole challenge:
◯ + ◯ = 8 = ◯ + ◯
◯ + ◯ = 3 = ◯ – ◯
◯ + ◯ = 12 = ◯ × ◯
◯ + ◯ = 1 = ◯ ÷ ◯
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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 3rd & 7th rows contain the following fourteen numbers:
4 11 13 24 25 27 30 36 42 45 66 70 77 80
What is the sum of the multiples of 12?
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 151, in FIVE different ways, when using Lagrange’s Theorem.
The Mathematically Possible Challenge
Using the three digits 2, 6 and 9 once each, with + – × ÷ available, find the SIX numbers it is possible to make from the list below:
1 3 6 10 15 21 28 36 45 55 66
#TriangularNumbers
The Target Challenge
Can you arrive at 151 by inserting 4, 6, 9 and 11 into the gaps on each line?
- ◯²+◯×◯+◯ = 151
- ◯²+◯×◯–◯ = 151
Answers can be found here.
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