Puzzle 197
Each of these words can have the same letter placed at the beginning and the end to form a new (common) word.
For example, -LIT- becomes ELITE by adding an E at both ends.
What are the new words?
-eve-
-able-
-carve-
-as-
-on-
-ode-
-elude-
-ape-
-ate-
-rod-
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Hint
One of the words starts and ends with T.
Answers
eve = level
able = tablet
carve = scarves
as = ease, hash, sass
on = gong, sons
ode = codec, modem
elude = deluded
ape = lapel
ate = dated, rater
rod = erode
Puzzle 198
Which word comes next in this sequence:
India · Victor · X-Ray · Lima · Charlie · ?
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Hint
Think of Roman numerals.
Answer
Delta.
Take the Roman numerals in sequence, and convert to the phonetic alphabet.
1 = I = India
5 = V = Victor
10 = X = X-Ray
50 = L = Lima
100 = C = Charlie
500 = D = Delta
Puzzle 199
I recently went to the shop and purchased 4 items.
Three of the items cost:
$1.50
$3.00
$4.00
There was quite a long queue, and as I was quite bored, I was playing with my pocket calculator while I waited.
Very curiously, the 4 prices added to the same number as I got when I multiplied the 4 prices together.
What was the price of the 4th item?
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Hint
What do the 3 numbers add to, and multiply to, so far?
Answer
$0.50.
Reasoning
The three prices add to 1.50 + 3.00 + 4.00 = 8.50.
The three prices multiply to 1.50 x 3.00 x 4.00 = 18.00.
You might be able to see that adding another 0.50 will take the total to 9.00, and multiplying by another 0.50 will take the product to 9.00.
The answer can also be found using algebra. If we call the missing price P, we have:
1.50 + 3.00 + 4.00 + P = 1.50 x 3.00 x 4.00 x P
8.50 + P = 18.00 x P
8.50 = 18.00 x P − P
8.50 = 17.00 x P
8.50 ÷ 17.00 = P
P = 0.50.
Puzzle 200
What is the smallest positive integer which …
… when multiplied by 3 gives a number consisting of only 4's?
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Hint
Try working backwards.
Answer
148.
Reasoning
A number that is divisible by 3 has digits that add up to a number that is also divisible by 3 (for example, 123 is divisible by 3).
So we can look for the first number where 4 + 4 + 4 + 4 + 4 + … is divisible by 3, which is 4 + 4 + 4, and 444 ÷ 3 = 148 .
Alternative Reasoning
Let's try the possible answers in order:
4 ÷ 3 = 1.3333
44 ÷ 3 = 14.6666
444 ÷ 3 = 148
Double-Checking
148 x 3 = 444.
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