Puzzle 49
I am compiling the new BrainBashers world almanac, and it now contains lots more pages.
I know that it takes 333 digits to print the page numbers in sequence.
How many numbered pages does the book have?
How many times does the number 3 appear?
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Hint
Think of the pages from 1-9, and then 10-99.
Answers
There are 147 pages.
The number 3 appears 35 times.
Answer #1
For pages 1-9, there are 9 pages, which is 9 digits.
For pages 10-99, there are 90 pages, which is 180 digits.
This is a total so far of 189, therefore we require another 333 – 189 = 144 digits, which is another 144 ÷ 3 = 48 pages.
Taking us to 9 + 90 + 48 = 147 pages in total.
Answer #2
From page 1 to 147 we have 15 pages that end in 3:
3, 13, 23, ..., 143
We also have the ten pages that start with 30:
30, 31, 32, ..., 39
Plus the ten pages that start with 130:
130, 131, 132, ..., 139
For a total of 15 + 10 + 10 = 35 number 3's.
Puzzle 50
Take a set of three letters from the left column, and a set of three letters from the right column and merge them together, without changing the order of the letters in each half (matching sets might not be on the same row).
Example 1: WMB + OAT and MAT + WOB both equal WOMBAT.
Example 2: RBT + ABI and AIT + RBB both equal RABBIT.
Can you find the six animals that have been split in half?
CYO ARU
WLS DNE
EAR FEE
OKY OTE
RRT JAR
AGU BVE
Puzzle Copyright © Kevin Stone
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Hint
The first letters of the words are: B, C, D, F, J, W.
Answers
Beaver, coyote, donkey, ferret, jaguar, walrus.
EAR + BVE = BEAVER
CYO + OTE = COYOTE
OKY + DNE = DONKEY
RRT + FEE = FERRET
AGU + JAR = JAGUAR
WLS + ARU = WALRUS
Puzzle 51
During a recent BrainBashers thinking contest(!), the total number of points scored by the first six players was 103 and every score was above zero.
The first player scored half the points of the second player, who in turn scored 6 points fewer than the third player.
The third player in turn scored two thirds the points of the fourth player.
The fifth player managed to score the same number of points as the difference between the first and fourth player's points.
Finally, the sixth player scored 14 fewer points than the fifth player.
Can you determine how many points the sixth player managed to score?
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Hint
The fourth player is the key to this tricky question.
Answer
9 points.
Respectively the scores were 7, 14, 20, 30, 23, 9.
Reasoning
If we label the six players A, B, C, D, E, and F, we know that:
[1] A + B + C + D + E + F = 103
and from the clues:
A = B ÷ 2
B = C – 6
C = D x 2 ÷ 3
E = D – A
F = E – 14
If instead we choose E = A – D, we'd later see that we end up with a negative value for E, which isn't allowed.
Since D is the letter we're missing information for, it's best to find all of the other letters in terms of D.
These steps are left as an exercise (use C in the equation for B, etc), but the result is:
A = ( D – 9) ÷ 3
B = (2D – 18) ÷ 3
C = (2D ) ÷ 3
D = (3D ) ÷ 3
E = (2D + 9) ÷ 3
F = (2D – 33) ÷ 3
Writing it as D = 3D ÷ 3 makes it slightly clearer to see, when adding in the next step.
We can then use these in [1] to find that 12D = 360, so D = 30.
Therefore, F = 9.
Puzzle 52
Bank Robbery #2 - Logic Puzzles
After a local bank robbery, four suspects were interviewed. Below is a summary of their statements.
The police know that each of them told the truth in one of the statements, but lied in the other.
From this information, can you tell who committed the crime?
Ashley said:
It wasn't Drew
It wasn't Billie
Billie said:
It wasn't Casey
It was Drew
Casey said:
It was Ashley
It wasn't Drew
Drew said:
It was Casey
It wasn't Ashley
Puzzle Copyright © Kevin Stone
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Hint
Remember that each of them told the truth in one of their statements, but lied in the other.
Answer
Billie robbed the bank.
Reasoning
We know that each of them told the truth in one of the statements and lied in the other.
So according to Ashley, as one of the statements is false, it must have been either Drew or Billie.
If it was Drew, then Billie's statements would both be true, which isn't allowed.
Therefore, it was Billie, which agrees with Casey and Drew's statements.
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