Puzzle 33
Cen yee rell wrer er wreng werr rrer peregrepr? Er ferrr glence yee mey rrenk rrer jerr rre vewelr reve preblemr, ber ne! Rrree cenrenenrr elre reve preblemr, rrey reve been repleced werr rre lerrer R, ber wrecr ener ere rrey?
Puzzle Copyright © Kevin Stone
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Hint
It's not just the vowels that have a problem.
Answer
H, S, and T.
It should read:
"Can you tell what is wrong with this paragraph? At first glance you may think that just the vowels have problems, but no! Three consonants also have problems, they have been replaced with the letter R, but which ones are they?"
Puzzle 34
What is the next number in the sequence:
32 35 40 44 52 112 {?}
Puzzle Copyright © Kevin Stone
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Hint
This is a tricky question related to number bases.
Answer
200.
Each number in the sequence is a representation of the number 32 in different bases, starting with base 10.
Base 10: 32 = 3 x 10^1 + 2 x 10^0 = 3 x 10 + 2 = 32
Base 9 : 35 = 3 x 9^1 + 5 x 9^0 = 3 x 9 + 5 = 32
Base 8 : 40 = 4 x 8^1 + 0 x 8^0 = 4 x 8 + 0 = 32
Base 7 : 44 = 4 x 7^1 + 4 x 7^0 = 4 x 7 + 4 = 32
Base 6 : 52 = 5 x 6^1 + 2 x 6^0 = 5 x 6 + 2 = 32
Base 5 : 112 = 1 x 5^2 + 1 x 5^1 + 2 x 5^0 = 1 x 25 + 1 x 5 + 2 = 32
Base 4 : 200 = 2 x 4^2 + 0 x 4^1 + 0 x 4^0 = 2 x 16 + 0 + 0 = 32
Puzzle 35
During a recent BrainBashers race meeting, the fastest driver managed to complete a lap with an average speed of 150 mph.
They managed to complete the first two fifths of the lap at a speed of 123 mph and the second two fifths of the lap at a speed of 164 mph.
At what speed was the final one fifth of the lap length covered?
Puzzle Copyright © Kevin Stone
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Hint
The answer is not 176 mph
Answer
205 mph.
Reasoning
Over the years I've had quite a few emails about this puzzle and many methods have been suggested but only the one below gives the correct answer.
If we take the number of miles in a lap to be L miles and use time = distance / speed.
The first 2/5 are covered at 123 mph. Therefore, the time taken was [(2/5) x L] / 123 hours.
The next 2/5 are covered at 164 mph. Therefore, the time taken was [(2/5) x L] / 164 hours.
The last 1/5 is covered at y mph. Therefore, the time taken was [(1/5) x L] / y hours.
The entire trip is covered at an average of 150 mph. we can conclude that:
2L 2L L L
————— + ————— + ——— = ———
5x123 5x164 5y 150
Rearranging and simplifying gives:
1 1 2 2
— = —— - ——— - ———
y 30 123 164
That means that y = 1 / (1/30 - 2/123 - 2/164)
Therefore y = 205.
Puzzle 36
What are the next five letters in this sequence:
JAJWUTH
TFAPOW
JFDABHC
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Hint
This is a well known nursery rhyme.
Answer
AJCTA.
These are the initial letters from the nursery rhyme 'Jack and Jill went up the hill'. The letters represent 'and Jill came tumbling after'.
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