Puzzle 1
Yesterday I was asked to buy some stamps.
In the land of BrainBashers, stamps are available in denominations of 3p, 9p, 11p, 17p, and 21p (just the five different values).
For three denominations of stamp I was asked to buy eight of each, and for the other two denominations I was asked to buy nine of each.
Unfortunately, I forgot which I was supposed to buy eight of, and which to buy nine of!!
Luckily I had been given the exact money required to buy the stamps, £5.00, 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 8 of each stamp.
Answer
Eight lots of 11p, 17p and 21p, and nine lots of 3p and 9p.
Reasoning
For three denominations of stamp I was asked to buy 8 of each, and for the other two denominations I had to buy 9 of each.
So I had to buy at least 8 of all five denominations.
This would be for a total of 8 x (3 + 9 + 11 + 17 + 21) = 488p = £4.88.
The remaining 12p has to buy the remaining 2 stamps, which must have been 3p and 9p.
Double-Checking
9 x 3 = 27
9 x 9 = 81
8 x 11 = 88
8 x 17 = 136
8 x 21 = 168
For a total of 27 + 81 + 88 + 136 + 168 = 500p = £5.
Puzzle 2
Three teachers were discussing how long they had been teaching.
Alex and Billie had been teaching for a total of 36 years.
Charlie and Billie had been teaching for a total of 22 years.
Charlie and Alex had been teaching for a total of 28 years.
How long had each been teaching?
Puzzle Copyright © Kevin Stone
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Hint
If we look at all of the clues, each person appears exactly twice.
Answer
Alex had been teaching for 21 years.
Billie had been teaching for 15 years.
Charlie had been teaching for 7 years.
Reasoning
If we look at all of the clues, each person appears exactly twice.
So the total of the three clues gives us two lots of Alex + Billie + Charlie = 36 + 22 + 28 = 86.
So, Alex + Billie + Charlie = 43 years.
In each clue we are given two of the people, so we can use this to find the missing person:
Charlie and Billie had been teaching for a total of 22 years, which means that Alex must be: 43 − 22 = 21 years.
Charlie and Alex had been teaching for a total of 28 years, which means that Billie must be: 43 − 28 = 15 years.
Alex and Billie had been teaching for a total of 36 years, which means that Charlie must be: 43 − 36 = 7 years.
Reasoning With Algebra
Let Alex = A, Billie = B and Charlie = C, then:
[1] A + B = 36
[2] C + B = 22
[3] C + A = 28
If we use [3] − [2] we have:
[4] A − B = 6
If we use [1] + [4] we have:
2A = 42
A = 21
By [1] B = 15. By [3] C = 7.
Puzzle 3
What word is missing from this sequence:
begin · inch · channel · elastic · ? · cellar · arisen · end
Puzzle Copyright © Kevin Stone
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Hint
Look closely at the beginnings and the ends of the words.
Answer
Ice.
Each word begins with the last two letters of the previous word.
Puzzle 4
Which is larger:
seconds in a week
minutes in a year
Puzzle Copyright © Kevin Stone
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Hint
There are 60 seconds in a minute, and 60 minutes in an hour.
Answer
Seconds in a week.
Reasoning
There are 60 x 60 x 24 x 7 = 604,800 seconds in a week.
There are 60 x 24 x 365 = 525,600 minutes in a (non-leap) year.
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