What four-digit number has Digit 1 three smaller than Digit 4, which is one more than Digit 2, which is twice Digit 3, which is one more than one third of Digit 4?
Answer
I asked for 9 foot 2 inches (110 inches) and my friend brought me 2 foot 9 inches (33 inches).
Reasoning
I asked my friend to buy me A feet and B inches, which is a total of 12A + B inches.
He accidentally bought me B feet and A inches, which is 12B + A inches.
We know that 12B + A is actually only 30% of what I wanted, so:
12B + A = 0.3 x (12A + B)
Multiply throughout by 10:
120B + 10A = 3 x (12A + B)
120B + 10A = 36A + 3B
117B = 26A
B = 26A ÷ 117
Don't forget that A and B can only be integers, and between 0 and 11.
Since 26 x A has to be at least 117, the lowest possible value for A is 5. We can check the remaining possibilities.
5 x 26 = 130
6 x 26 = 156
7 x 26 = 182
8 x 26 = 208
9 x 26 = 234 (*)
10 x 26 = 260
11 x 26 = 286
The only number wholly divisible by 117 is 234, which means that A = 9, and B = 2.
So, I originally asked for 9 feet 2 inches.
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Puzzle 103
Alex likes soda very much. At the local convenience store, for every 5 empty soda bottles the reward is a full fresh bottle.
As part of a local recycling initiative, Alex collected 77 empty bottles.
How many bottles of soda could Alex drink in total?
Reasoning
From the initial 77 bottles, 75 bottles can be recycled for 15 new full bottles.
Once those are drunk, Alex will have 17 empty bottles (15 plus the 2 extra empty bottles).
From the 17 empty bottles, 15 bottles can be recycled for 3 new full bottles.
Once those are drunk, Alex will have 5 empty bottles (3 plus the 2 extra empty bottles), which can be recycled for one final full bottle.
Giving a total of 15 + 3 + 1 = 19.
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Puzzle 104
In this long division, each number has been replaced by another. The answer has also been removed. Can you determine the answer?
....
———————
75 | 796767
791
——
57
30
——
86
82
——
47
47
——
9
