Tag Archives: BL puzzles

Sheep in Garden Problem

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This is a slightly challenging problem from BL’s Math Games.

“In a square garden ABCD of side 10m, a sheep sets off from B and moves along BC at 30cm per minute.  At the same time, you set off from C and move along edge CD at 40cm per minute.  The question is, what’s the shortest distance between you and the sheep in meters?

This is somewhat an optimization problem because as you and the sheep move along the sides of the square at different rates, the distance in between varies as you can imagine.”

There’s at least one non-calculus solution and of course one calculus solution.

Answer.

See Sheep in Garden Problem for solutions.

Whose Bullet?

Here is a probability problem from BL’s Weekly Math Games.  Normally I am not a fan of such problems, but this one seemed fairly straight-forward for a change.

“I hit the target 75% of the time. You hit the target 25% of the time.  We aim at the same time, and only one bullet hits.  What’s the probability it came from me?

Now as for this puzzle, it would be tempting to think that I am 3 times as good at hitting the target, but I am not!”

Answer.

See Whose Bullet for a solution

Sphere and Plane Puzzle

This is another puzzle from BL’s Weekly Math Games.

“a + b + c = 2, and

a2 + b2 + c2 = 12

where a, b, and c are real numbers.  What is the difference between the maximum and minimum possible values of c?”

The original problem statement mentioned a fourth real number d, but I considered it a typo, since it was not involved in the problem.

Answer.

See Sphere and Plane Puzzle for a solution.