Working systematically
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problemAdjacent Additions
In a 7-digit numerical code, each group of four consecutive digits adds to 16, and each group of five consecutive digits adds to 19. What is the sum of all 7 digits?
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problemEnd of a Prime
I made a list of every number that is the units digit of at least one prime number. How many digits appear in the list?
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problemThrees and Fours
What is the smallest integer where every digit is a 3 or a 4 and it is divisible by both 3 and 4?
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problemOlympic Magic
in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?
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problemMagic W
Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.
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problemTetrahedra Tester
An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?
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problemTwin Line-Swapping Sudoku
A pair of Sudoku puzzles that together lead to a complete solution.
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problemFacial Sums
Can you make the numbers around each face of this solid add up to the same total?