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A 'complete' word is a word in which every letter, in turn, can be replaced by another to form a new word.
For example, SEND is a complete word because:
Starting with SEND we can replace the S with an L to make LEND
Starting with SEND we can replace the E with an A to make SAND
Starting with SEND we can replace the N with an E to make SEED
Starting with SEND we can replace the D with a T to make SENT.
Which 2 of the following words are not complete words? Proper nouns (i.e. people's names) are not allowed.
Hint: As an example, the letters of HARD can be changed, in turn, to give CARD, HERD, HAND, HARP.
Answer: HANG and LEAN.
The remaining 8 words can be changed as follows:
HARD >> CARD, HERD, HAND, HARP
PORT >> FORT, PART, POET, PORE
DUCK >> MUCK, DECK, DUSK, DUCT
BAIL >> HAIL, BOIL, BAWL, BAIT
MAST >> CAST, MOST, MALT, MASK
THIN >> SHIN, TWIN, THAN, THIS
FIRE >> HIRE, FARE, FIVE, FIRM
READ >> BEAD, ROAD, REED, REAL
You have to be able to change EVERY letter to make a new word, so from HANG you can change H to make SANG, the A to make HUNG, and the G to make HAND, but you can't change the N to make a new word.
Puzzle 74
Alex and Blake were rowing their canoe along the River Trent.
In the morning they managed to row upstream at an average speed of 2 miles per hour.
They then stopped for a spot of lunch and a nice rest.
In the afternoon, the pace was a little easier as they were now rowing downstream back to their starting point, and managed an average speed of 4 miles an hour.
The morning trip took them 3 hours longer than the afternoon.
Hint: You can either fix the distance rowed and see what numbers work, or you can fix the number of hours.
Answer: 12 miles.
In the morning, rowing at 2 miles per hour, they rowed for 6 hours. In the afternoon, rowing at 4 miles per hour, they rowed for 3 hours.
There are a number of ways of working this out, and here are two of them:
Method 1
If we assume the distance the rowed upstream to be D miles, we know the morning took (D ÷ 2) hours, and the afternoon took (D ÷ 4) hours, with a difference of 3 hours. So:
D D 3
   =
2 4
Multiplying throughout by 2, and then 4, gives:
4D  2D = 24
So:
2D = 24
And:
D = 12 miles.
They rowed 12 miles upstream.
Method 2
If we assume they rowed for H hours upstream, we know they travelled H x 2 miles in the morning. In the afternoon they rowed for (H  3) hours, and travelled (H  3) x 4 miles. We know these distances are the same, so:
2H = (H  3) x 4
Giving:
2H = 4H  12
Rearranging gives:
12 = 2H
So:
H = 6 hours.
They rowed for 6 hours upstream at 2 miles per hour, which is a total of 12 miles.
Puzzle 75
Starting in the bottom left corner and moving either up or right, adding up the numbers along the way, what is the largest sum which can be made?
The terminal letters of the words one, two, three.
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