Puzzle 185
Which is larger:
3 raised to the 5th power
5 raised to the 3rd power
Puzzle Copyright © Kevin Stone
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Hint
3 raised to the 5th power is 3 x 3 x 3 x 3 x 3.
Answer
3 raised to 5th power.
Reasoning
3 raised to the 5th power = 3 ^ 5 = 3 x 3 x 3 x 3 x 3 = 243
and
5 raised to the 3rd power = 5 ^ 3 = 5 x 5 x 5 = 125.
Puzzle 186
At a recent visit to the reptile house at the local animal sanctuary, I counted a total of 27 heads and 70 feet.
I was counting snakes, lizards, and people and I know that there were exactly twice as many lizards as people.
How many snakes did I count?
Puzzle Copyright © Kevin Stone
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Hint
Snakes don't have legs.
Answer
6 snakes, along with 7 people and 14 lizards.
Reasoning
We know that for each person (2 legs) there were 2 lizards (4 legs each).
Which means for every person, we can count a total of 10 legs.
Snakes don't have legs, so the total of 70 legs must have been 7 people (and 14 lizards).
This is a total of 21 heads, so the remaining 6 heads were all snakes.
Double-Checking
7 people gives 7 heads and 14 feet.
14 lizards gives 14 heads and 56 feet.
6 snakes gives 6 heads and 0 feet.
For a total of 6 + 7 + 14 = 27 heads, and 0 + 14 + 56 = 70 feet.
Puzzle 187
Yesterday I was asked to buy some stamps.
In the land of BrainBashers, stamps are available in denominations of 4p, 5p, 7p, 12p, and 19p (just the five different values).
For three denominations of stamps, I was asked to buy six of each. For the other two denominations. I was asked to buy ten of each.
Unfortunately, I forgot which I was supposed to buy six of, and which to buy ten of!
Luckily I had been given the exact money required to buy the stamps, £3.50, so the shopkeeper was able to work out the stamps I needed.
Which stamps did I have to buy?
Puzzle Copyright © Kevin Stone
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Hint
I bought at least 6 of each stamp.
Answer
Six lots of 4p, 7p, and 19p, and ten lots of 5p, and 12p.
Reasoning
For three denominations of stamps, I was asked to buy 6 of each, and for the other two denominations, I had to buy 10 of each.
So I had to buy at least 6 of all five denominations.
This would be for a total of 6 x (4 + 5 + 7 + 12 + 19) = 282p = £2.82.
The remaining 68p has to buy the remaining 8 stamps, 4 of each of the two remaining denominations.
If we just bought 1 of each of the two remaining denominations they would have cost 68 ÷ 4 = 17p.
So the two remaining denominations must have been 5p and 12p.
Double-Checking
6 x 4 = 24
10 x 5 = 50
6 x 7 = 42
10 x 12 = 120
6 x 19 = 114
For a total of 24 + 50 + 42 + 120 + 114 = 350p = £3.50.
