Puzzle 57
What word goes in the brackets:
food [road] hard
weep [----] fall
Puzzle Copyright © Kevin Stone
workings
hint
answer
print
www.brainbashers.com
/puzzle/zvus
share
Hint
The letters come from the two words on the outside.
Answer
Leap.
From the third letter of the second word, plus the third letter of the first word, plus the second letter of the second word, plus the fourth letter of the first word.
Puzzle 58
What is missing from this sequence:
teloiv · ogidni · eulb · ? · wolley · egnaro · der
workings
hint
answer
print
www.brainbashers.com
/puzzle/zvuz
share
Hint
Look to the skies for the answer.
Answer
neerg.
These are the colours of the rainbow reversed.
Puzzle 60
As my autumnal birthday approaches I like to collect leaves! A little bizarre perhaps, but I enjoy it!
Starting on the first day of the month I collect 1 leaf, on the second day I collect 2 leaves, the third day I collect 3 leaves, and so on.
On my birthday, I will have collected 276 leaves altogether. Which day of the month is my birthday?
Bonus Question: how many days would it take for me to collect 56,616 leaves?
Puzzle Copyright © Kevin Stone
workings
hint
answer
print
www.brainbashers.com
/puzzle/zquz
share
Hint
How many leaves will I have collected on day 5?
Answer
On the 23rd .
Reasoning
We could simply keep adding until we get the required number:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23
= 276 leaves.
But a more mathematical method might help to answer the Bonus Question, as this might take a while if we keep adding!
So, let's create a method by imagining that we are adding the numbers from 1 to 30.
1 + 2 + 3 + … + 28 + 29 + 30
If we now take the numbers in pairs, taking one from each end, we have:
(1 + 30) + (2 + 29) + (3 + 28) + … + (15 + 16)
Each pair adds to 31, and we have 15 pairs. So the total sum is 31 x 15 = 465.
The total sum from 1 to any number (N) can be found using this technique, and we will have:
Each pair adds to (1 + N), and there are N ÷ 2 pairs. So the total is:
(1 + N) x N
—
2
In this puzzle, we know that this equals 276.
So:
(1 + N) x N = 276
—
2
We can expand the brackets, and multiply both sides by 2, to give:
N + N2 = 552
Rearranging we get:
N2 + N − 552 = 0
And 552 = 2 x 2 x 2 x 3 x 23, so this can be factorised as:
(N + 24) x (N − 23) = 0
Because we need to find a positive number of days, the only possible answer is:
(N − 23) = 0
So N = 23 days.
Bonus Question
To answer the bonus question, we have:
(1 + N) x N = 56616
—
2
Rearranging we get:
N2 + N − 113232 = 0
And 113232 = 24 x 3 x 7 x 337, so this can be factorised as:
(N − 336) x (N + 337) = 0
Because we need to find a positive number of days, the only possible answer is:
(N − 336) = 0
So N = 336 days (I did say that I liked collecting leaves!).
next >