Puzzle 49
Three teachers were discussing how long they had been teaching.
Alex and Blake had been teaching for a total of 36 years.
Charlie and Blake 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.
Blake 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 + Blake + Charlie = 36 + 22 + 28 = 86.
So, Alex + Blake + 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 Blake 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 Blake must be: 43 - 28 = 15 years.
Alex and Blake 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, Blake = 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 50
Each empty white square in the grid contains one of the numbers 1, 2, 3,..., 8. Each of the horizontal and vertical equations must be true, and each number must be used exactly once.
Puzzle Copyright © Erich Friedman
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Hint
The top-left square contains the 6.
Answer
Puzzle 51
Many years ago, a cruise liner sank in the middle of the ocean.
The castaways luckily landed on a remote desert island.
There was enough food for the 220 people to last three weeks.
Six days later a rescue ship appeared, unluckily this ship also sank, leaving an additional 55 people stranded on the island to now share the original rationed food.
The food obviously had to be re-rationed, but everyone was now on one-half of the original ration, so how many days in total would the food last for, from the day of the original sinking?
Puzzle Copyright © Kevin Stone
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Hint
How many rations were there at the start?
Answer
30 days.
Reasoning
Originally there was enough food for 220 people for 21 days, which totals 4620 rations.
After 6 days 1320 rations were eaten.
Therefore, there were now 3300 rations for 275 people, which would last for another 24 days at one-half ration per person.
Which is 30 days in total from the original sinking.
Puzzle 52
A local angler caught a large trawler load of haddock.
They decided to donate some of the fish to the local community, 1,672 people in all.
Every person over 50 received 16 fish, and to every person under 50 received 96 fish.
Only 3/4 of the over 50s collected their haddock, and only 1/8 of the under 50s collected their fish.
How many fish did the angler give away?
Puzzle Copyright © Kevin Stone
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Hint
Try a random number of over 50s to see what happens.
Answer
20,064 fish.
Reasoning
As only 3/4 of the over 50s claimed 16 fish, this averages out to 12 fish each.
Similarly only 1/8 of the under 50s claimed 96 fish, this again averages out to be 12 fish each.
Therefore the total number of fish was 1,672 x 12 = 20,064.
It doesn't matter how many over/under 50s there are.
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