T he Main Challenge
Can you place the 16 numbers 0 0 1 1 2 2 3 4 4 5 6 7 7 8 9 9 into the 16 gaps below so all four lines work out arithmetically?
◯ + ◯ = 9 = ◯ + ◯
◯ + ◯ = 7 = ◯ – ◯
◯ + ◯ = 12 = ◯ × ◯
◯ + ◯ = 6 = ◯ ÷ ◯
If you enjoyed this number puzzle, click Mathelona for details of similar challenges.
The 7puzzle Challenge
The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 2 up to 84.
The 2nd & 5th rows contain the following fourteen numbers:
6 7 8 16 17 21 28 48 50 55 63 64 81 84
What is the sum of the square numbers?
The Lagrange Challenge
Lagrange’s Four-Square Theorem states that every positive 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).
There are SEVEN ways of making 102 when using Lagrange’s Theorem. Can you find them all?
The Mathematically Possible Challenge
Using 5, 7 and 10 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?
40 41 42 43 44 45 46 47 48 49
#NumbersIn40s
The Target Challenge
Can you arrive at 102 by inserting 3, 4, 6 and 10 into the gaps on both lines?
- (◯+◯+◯)×◯ = 102
- ◯²+◯×◯÷◯ = 102
Answers can be found here.
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