Reasoning
Each term increases by the number of letters in the previous term (ignoring any hyphens).
1 + length("ONE") = 4
4 + length("FOUR") = 8
8 + length("EIGHT") = 13
13 + length("THIRTEEN") = 21
21 + length("TWENTYONE") = 30
30 + length("THIRTY") = 36
36 + length("THIRTYSIX") = 45
??
Puzzle 3
Practical Pat was asked to cut a 99-foot rope into three smaller, equal length ropes.
However, as usual, Pat couldn't find the measuring tape, so a guess took place!
When the tape was finally found (it was under a hat), Pat discovered that:
the second piece of rope was twice as long as the first piece, minus 35 feet the third piece of rope was half the length of the first, plus 15 feet
How long were each of the pieces of rope?
Answer
First = 34 feet.
Second = 33 feet.
Third = 32 feet.
Reasoning
This question can be solved using algebra. If we call the length of the first rope A, we have: Rope 1 = A Rope 2 = 2 x A − 35 Rope 3 = 0.5 x A + 15
The three ropes add to 99 feet: 99 = Rope 1 + Rope 2 + Rope 3 99 = A + (2 x A − 35) + (0.5 x A + 15) 99 = 3.5 x A − 20 119 = 3.5 x A 34 = A
At the recent spring fayre, four keen gardeners were displaying their fine roses.
In total there were four colours and each rose colour appeared twice.
From the clues below, can you tell who had which colour roses?
Gardener Green had a yellow rose. Gardener Yellow did not have a red one. Gardener Red had a blue rose, but not a green one. Gardener Blue did not have a yellow one. One person with a red rose also had a green one. One person with a yellow rose also had a blue one. One of the persons with a green rose had no red. Neither of the persons with a yellow rose had a green one. No person had two roses of the same colour. No two persons had the same two colour roses, and their names provide no clues.
