Puzzle 1
Below, 10 countries have been broken into chunks of letters.
The chunks have been moved around, no chunk is used twice, and all of the chunks are used.
Can you determine what the 10 countries are?
ezu itz zil ela bra gi ia
fi pan mba bel and ber zi
nl bo cam ven dia and um
sw bwe mex erl ico ja li
Puzzle Copyright © Kevin Stone
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Hints
The countries begin with the letters: B, M, B, J, C, S, Z, V, F, L.
Answers
bel-gi-um = Belgium
mex-ico = Mexico
bra-zil = Brazil
ja-pan = Japan
cam-bo-dia = Cambodia
sw-itz-erl-and = Switzerland
zi-mba-bwe = Zimbabwe
ven-ezu-ela = Venezuela
fi-nl-and = Finland
li-ber-ia = Liberia
Puzzle 2
Can you find three consecutive odd numbers that …
… total 1,287 when multiplied together?
Puzzle Copyright © Kevin Stone
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Hint
There are two different methods, one involves a cube root, and the other doesn't require a calculator.
Answer
9 x 11 x 13.
Reasoning #1
We're after three numbers that multiply together, so a good place to start is the cube root of 1,287, which is roughly 10.88.
Let's try dividing by the closest odd number to 10.88:
1287 ÷ 11 = 117
We're now after whole divisors of 117. Trying the odd numbers either side of 11 might work.
Trying either 9 or 13 gives the answer:
9 x 11 x 13 = 1,287
Trying the closest odd number to the cube root always works, and the other two numbers are the odd numbers either side.
Reasoning #2
We after three numbers that multiply together, but none of these can end in 5 (otherwise our answer would end in 0 or 5).
So, they can only end in 7, 9, 1 (e.g. 87, 89, 91), or 9, 1, 3 (e.g. 89, 91, 93).
However, if they ended in 7, 9, 1, the answer would end in 3 (because 7 x 9 x 1 = 63).
Therefore, they end in 9, 1, and 3 (because 9 x 1 x 3 = 27).
The first numbers we can try are 9, 11, 13:
= 9 x 11 x 13
= 99 x 13
= 100 x 13 − 13
= 1300 − 13
= 1,287
A calculator is not required!
Puzzle 3
If York is 9 miles away, London is 14 miles and Manchester is 23 miles away.
How far away is Leeds?
Puzzle Copyright © Kevin Stone
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Hint
Consonants and vowels (AEIOU) are each worth something.
Answer
12 miles away.
Consonants are worth 2 and vowels (AEIOU) are worth 3.
Double-Checking
York
3C + 1V = 3 x 2 + 3 = 9
London
4C + 2V = 4 x 2 + 2 x 3 = 14
Manchester
7C + 3V = 7 x 2 + 3 x 3 = 23
Leeds
3C + 2V = 3 x 2 + 2 x 3 = 12
Puzzle 4
What are the next two numbers in this sequence:
14 · 91 · 62 · 53 · 64 · 96 · ? · ?
Puzzle Copyright © Kevin Stone
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Hint
Try removing the spaces between the numbers.
Answer
48 and 11.
Reasoning
These are the squares of numbers without the correct spacing.
1 4 9 16 25 36 49 64 81 100
with no spaces becomes:
149162536496481100
broken into blocks of two:
14 91 62 53 64 96 48 11 00
So the next two in the sequence are 48 and 11.
