Puzzle 29
In this puzzle, all of the numbers from 1 to 8 are used.
The differences (larger - smaller) between any two connected numbers are all different.
Can you complete the grid?
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Hint
What are the possible differences?
Answer
Reasoning
The first observation is that all of the possible gaps must exist: 1, 2, 3, 4, 5, 6, 7, and let's call these Gap1, ..., Gap7.
Looking at Gap7, this can only happen when:
[Gap7a: 1 is next to 8]
Looking at Gap6, this can happen when:
[Gap6a: 1 is next to 7]
this is not allowed because 1 and 7 are given squares that are not next to each other.
[Gap6b: 2 is next to 8]
Looking at Gap5, this can happen when:
[Gap5a: 1 is next to 6]
[Gap5b: 2 is next to 7]
this is not allowed because [Gap6b: 2 is next to 8], which would mean that we can't also have [Gap7a: 1 is next to 8].
[Gap5c: 3 is next to 8]
this is not allowed because we couldn't then also have: [Gap7a: 1 is next to 8] and [Gap6b: 2 is next to 8].
We can't have the 8 above the 1, as there is then no place for [Gap6b: 2 is next to 8].
So, we have two possible places for the 8, to the left of the 1, or to the right of the 1.
8 to the left of 1
What can we place to the right of 1?
3 – no, because the gap between the 1 and 3, and the gap between 3 and 5, are both 2.
4 – no, because the gap between 4 and 5 is 1, which we already have.
6 – no, because the gap between 5 and 6 is 1, which we already have.
So the 8 can't go to the left of 1.
8 to the right of 1
We know [Gap5a: 1 is next to 6].
Let's try 6 to the left of 1. No matter where we place the 3 and 4 we end up with duplicate gaps. So this doesn't work.
So, the 6 must go above 1, but the 4 can't go to the left of 1 because of duplicate gaps. Therefore, this doesn't work either.
Which means that the final answer is:
Puzzle 30
By changing the third letter of each of the words below, can you make another valid word?
You have to change each word such that the third letters will reveal a ten-letter word when read downwards.
Therefore, what now reads KRZSAPROKD will be a real word.
BAKE
CURE
MAZE
PEST
NEAT
ROPE
PORT
FOOD
POKE
SODA
Puzzle Copyright © Kevin Stone
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Hint
The first word is BASE.
Answer
Strawberry.
BAKE = BASE
CURE = CUTE
MAZE = MARE
PEST = PEAT
NEAT = NEWT
ROPE = ROBE
PORT = POET
FOOD = FORD
POKE = PORE
SODA = SOYA
Puzzle 31
Hidden below are eight, 7-letter words.
Each word begins with the central S and you can move one letter in any direction to the next letter.
Each of the letters is used exactly once.
What are the words?
G |
N |
L |
K |
R |
T |
E |
E |
I |
E |
O |
X |
A |
E |
K |
R |
N |
I |
H |
M |
N |
E |
A |
Y |
S |
E |
A |
P |
R |
E |
P |
P |
A |
W |
O |
N |
E |
A |
G |
U |
E |
O |
R |
N |
E |
S |
A |
D |
E |
Puzzle Copyright © Kevin Stone
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Hint
One of the words is SAUSAGE.
Answer
Sixteen, shampoo, seaweed, sausage, spanner, speaker, syringe, snorkel.
Puzzle 32
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?
Puzzle Copyright © Kevin Stone
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Hint
Think of the pages from 1-9, and then 10-99.
Answer
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.
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