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If ca+b=56 and ab+c=29, then what is the value of ba+c?
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Five monkeys in a circus are sitting in the following order:
The ringmaster wants to reverse their order, but only by swapping the positions of two monkeys at a time.
This is one way, where two swaps take place:
1 2 |
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Another possible way takes exactly four swaps:
1 2 3 4 |
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Is it possible to do this in exactly three swaps?
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The blue figure is made of five quarter-circle arcs (each with integer radius) and a segment of length 4, which is the base of a 4×4 square grid.
What is the area of the blue figure?
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An infinite triangular lattice consists of points spaced 1 unit apart.
What is the probability (as a percentage) that a circle of unit diameter placed randomly in the lattice encloses no lattice points, as shown?
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11, 12, 21, 13, 22, 31, 14, 23, 32, 41, …
If 19201887 is the mth term and 20181789 is the nth term of the sequence above, find ∣m−n∣.
Note: In this sequence, the fractions do not reduce. For example, 22 is distinct from 11.
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