Puzzle 101

Practical Peter was asked to cut a 99 foot rope into three smaller, equal length ropes.
However, as usual, Pete couldn't find his measuring tape so he guessed!
When he finally did find his tape (it was under his hat), he discovered that:
A) the second piece of rope was twice as long as the first piece, minus 35 feet (i.e. 2 x first, - 35).
B) the third piece of rope was half the length of the first, plus 15 feet (i.e. 0.5 x first, + 15)
How long were each of the pieces of rope?

[Ref: ZGCD] © Kevin Stone

Hint: Only one of the ropes was 33 feet.

Answer:
First = 34 feet.

Second = 33 feet.

Third = 32 feet.

This question can be solved easily 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 = 1 ÷ 2 x A + 15
The three ropes add to 99 feet, so:
99 = Rope 1 + Rope 2 + Rope 3
99 = A + (2 x A - 35) + 1 ÷ 2 x A + 15
99 = 3.5 x A - 20
Adding 20 to both sides we have:
119 = 3.5 x A
So:
A = 119 ÷ 3.5
A = Rope 1 = 34 feet
Rope 2 = 2 x 34 - 35 = 68 - 35 = 33 feet
Rope 3 = 1 ÷ 2 x A + 15 = 1 ÷ 2 x 34 + 15 = 17 + 15 = 32 feet
Just to check:
Rope 1 + Rope 2 + Rope 3 = 34 + 33 + 32 = 99.
As required. QED.

Puzzle 102

Below you will find 15 well-known six letter words, with only their endings remaining. Can you determine the words?

...amt
...nue
...rtz
...oze
...mth
...iek
...gry
...thm
...koo
...spy
...sip
...lem
...uid
...tyr
...meg

[Ref: ZNFZ] © Kevin Stone

Hint: The first 6 words begin with the letters D, A, Q, S, W, S.

Answer: ...amt >> dreamt
...nue >> avenue
...rtz >> quartz
...oze >> snooze
...mth >> warmth
...iek >> shriek
...gry >> hungry
...thm >> rhythm
...koo >> cuckoo
...spy >> crispy
...sip >> gossip
...lem >> emblem
...uid >> liquid
...tyr >> martyr
...meg >> nutmeg

Puzzle 103

During the recent BrainBashers netball competition, 6 schools were competing.
Each school played each other once, with 2 points for a win, 1 point for a draw, 0 points if they lost.
Here are the final points after all of the matches:

Biddulph 4
Congleton 7
Astbury 9
Burslem 5
Stoke 1
Newcastle ?

How many points did Newcastle get?

[Ref: ZXFS] © Express Newspapers [Author: Kevin Stone]

Hint: How many teams were there? How many games were played?

Answer:
Since there were 6 teams, and every team played every other.
This is a total of 15 matches, with a total of 30 points.
Since the other teams scores add to 26, Newcastle scored 4 points.

Puzzle 104

Can you find the anagrams of the following words?

COAGULATE
CAVITATES
BACTERIAL
BALANCERS
HEADLAMPS
MILESTONE
TELEPHONY
DIGNIFIES
UNNOTICED

[Ref: ZKRV] © Kevin Stone

Hint: Each word only has one anagram.

Answer: CATALOGUE
ACTIVATES
CALIBRATE
BARNACLES
LAMPSHADE
LIMESTONE
POLYTHENE
SIGNIFIED
CONTINUED

Puzzle 105

Using the BrainTracker grid below, how many words can you find? Each word must contain the central P and no letter can be used twice. The letters do not have to be connected. Proper nouns are not allowed, however, plurals are. Can you find the nine letter word?
Excellent: 22 words. Good: 19 words. Average: 15 words.

[Ref: ZPVV] © Kevin Stone

Hint: Every word must contain the central letter.

Answer: Primitive.
Common words:
imp, per, perm, permit, pert, pet, pi, pie, pier, pit, prim, prime, PRIMITIVE , privet, rep, rip, ripe, temp, tip, trip, tripe, viper.
All words:
imp, impi, pe, per, peri, perm, permit, pert, pet, pi, pie, pier, pit, pitier, prim, prime, primi, PRIMITIVE , privet, rep, rip, ripe, temp, tempi, tip, tipi, trip, tripe, viper.