BrainTwister #78: One on top

#78 One on top

Set by Howard Williams

It is possible to write any number as a sum of unit fractions (fractions with 1 on top) with different denominators. For example, 3/5 = 1/2 + 1/10.

Starting from the expression 1 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6, can you combine the sixths together by adding, to make three unit fractions of different sizes that sum to 1?

If you begin instead with 12 twelfths, can you combine them to find a set of four different unit fractions that total 1?

How many other sets of four different unit fractions that add up to 1 can you find?

Solution next week

#77 Folded stacks

Solution

The three words are CARTHORSE, CAUTIONED and GNARLIEST.

For the third puzzle, the final step involves folding a 2-by-1 section in half, but tucking one half between the layers of the other.