Puzzle 117
This BrainBashers safe has a rather unusual control panel.
In order to open the safe, you have to press every single square once only, in the correct sequence, ending on the square marked E.
Each square indicates which square to press next, for example, 2U means move up 2 squares and 3R means move right 3 squares.
Can you determine which square you must start with?
| 4R |
4D |
1R |
1D |
2D |
4L |
1D |
| 1R |
4D |
5D |
2R |
2D |
1L |
4L |
| 2R |
1D |
1L |
2R |
2R |
2D |
2U |
| 2R |
2R |
3U |
3D |
1R |
3U |
6L |
| 3U |
3R |
1D |
2U |
4L |
2D |
3L |
| 3U |
1L |
1R |
1R |
1R |
1R |
2U |
| 6U |
E |
2U |
2L |
4L |
1L |
2U |
Note: this puzzle is not interactive, and the safe buttons cannot be clicked.
Puzzle Copyright © Kevin Stone
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Share link: https://www.brainbashers.com/puzzle/zixy
Hint
Start on any square, and see how far you get.
Answer
Start from the 2U in the bottom right-hand corner.
Puzzle 118
Below you will find ten common 6-letter words, however, every other letter is missing.
Can you determine the original words?
-s-e-d
-p-a-g
-r-f-r
-y-r-d
-r-f-e
-a-b-n
-a-e-a
-o-d-g
-s-f-l
-i-s-e
Puzzle Copyright © Kevin Stone
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Share link: https://www.brainbashers.com/puzzle/zagd
Hint
The first word begins with the letter A.
Answers
-s-e-d = ascend
-p-a-g = sprang
-r-f-r = prefer
-y-r-d = hybrid
-r-f-e = trifle
-a-b-n = carbon
-a-e-a = camera
-o-d-g = hotdog
-s-f-l = useful
-i-s-e = tissue
Puzzle 119
Tommy: "How old are you, mamma?"
Mamma: "Let me think, Tommy. Well, our three ages add up to exactly seventy years."
Tommy: "That's a lot, isn't it? And how old are you, papa?"
Papa: "Just six times as old as you, my son."
Tommy: "Shall I ever be half as old as you, papa?"
Papa: "Yes, Tommy; and when that happens our three ages will add up to exactly twice as much as to-day."
Tommy: "And supposing I was born before you, papa; and supposing mamma had forgot all about it, and hadn't been at home when I came; and supposing--"
Mamma: "Supposing, Tommy, we talk about bed. Come along, darling. You'll have a headache."
Now, if Tommy had been some years older he might have calculated the exact ages of his parents from the information they had given him. Can you find out the exact age of mamma?
Mamma's Age – Amusements In Mathematics, Henry Ernest Dudeney.
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Share link: https://www.brainbashers.com/puzzle/zpyu
Hint
The answer isn't a whole number of years, and algebra might be required.
Answer
29 years 2 months.
Reasoning #1
This answer is taken directly from the original book.
The age of Mamma must have been 29 years 2 months; that of Papa, 35 years; and that of the child, Tommy, 5 years 10 months. Added together, these make seventy years. The father is six times the age of the son, and, after 23 years 4 months have elapsed, their united ages will amount to 140 years, and Tommy will be just half the age of his father.
Reasoning #2
Here's my answer, with a little algebra.
If we call Tommy T, Mamma M and Papa P we can see that:
"our three ages add up to exactly seventy years" gives us:
(1) T + M + P = 70
"Just six times as old as you" gives us:
(2) P = 6 x T
In an unknown number of years (Y) "Shall I ever be half as old as you" gives us:
(3) P + Y = 2 x (T + Y)
and "our three ages will add up to exactly twice as much as today" gives us:
(T + Y) + (M + Y) + (P + Y) = 140
which can be written as
(4) T + M + P + 3Y = 140
We can see from (4) and (1) that
3Y = 70
so
(5) Y = 70 ÷ 3
Using (2) and (5) in (3) we have
P + Y = 2 x (T + Y)
6 x T + 70 ÷ 3 = 2 x (T + 70 ÷ 3)
4 x T = 70 ÷ 3
(6) T = 70 ÷ 12
We can now use (6) in (2) to see that:
P = 6 x T
P = 6 x 70 ÷ 12
P = 70 ÷ 2
And using the values for T and P in (1) we have:
T + M + P = 70
70 ÷ 12 + M + 70 ÷ 2 = 70
Multiply throughout by 12 to give:
70 + 12 x M + 420 = 840
12 x M = 840 – 420 – 70
12 x M = 350
M = 350 ÷ 12
So:
Tommy = 70 ÷ 12 = 5.83333 = 5 years 10 months.
Papa = 70 ÷ 2 = 35 = 35 years.
Mamma = 350 ÷ 12 = 29.1666 = 29 years 2 months.
Puzzle 120
Imagine a bottle recycling skip, empty other than one lonely bottle.
Every hour, on the hour, people come and put bottles into the skip.
The first hour, at noon, one person came and put a bottle in.
One hour later, two people each placed a bottle into the skip.
An hour later, four people each placed a bottle into the skip.
This doubling of people continued until 11pm, when the skip was finally full.
When was the skip exactly half full?
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Hint
Remember that the bottle count doubles each time.
Answer
10pm.
Reasoning
The skip started with 1 lonely bottle.
At Noon: 1 person came along and added a bottle, making the total 2 bottles.
At 1pm: 2 people came along and each added a bottle, making the total 2 + 2 = 4 bottles.
At 2pm: 4 people came along and each added a bottle, making the total 4 + 4 = 8 bottles.
At 3pm: 8 people came along and each added a bottle, making the total 8 + 8 = 16 bottles.
Therefore, the number of bottles in the skip is doubling every hour, as it was full at 11pm, it must have been half full at 10pm.
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