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#156 L of a puzzle

At first glance, you wouldn’t think it was possible to put these three L-shaped tetrominoes together to make a flat, symmetrical shape.

And yet, it turns out that there are two different ways to make a shape with mirror symmetry using all three Ls. Can you find them?

Hint: one solution looks a bit fishy, but you might love the other one.

Solutions next week

#155 Mother Hubbard

Solution

Ada is 55 and Betty is 33. Let Ada’s age be A and Betty’s age be B. This table shows the relationship between their ages:

Past Now Future

Ada B A 77

Betty A/5 B A

The difference between Ada’s and Betty’s ages remains constant, so B – A/5 = A – B = 77 – A.

If B – A/5 = A – B, the following is also true: 2B = A + A/5 = 6A/5. So B = 6A/10 = 0.6A

A – B = 77 – A, so we substitute 0.6A for B, giving us: A – 6A/10 = 77 – A, which we can turn into:

A + A – 6A/10 = 77, then into:

14A/10 = 77, which leads to:

A = 77 x 10/14. So A = 55. We know that B = 0.6A, so B = 33.