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Across: DUCK, PLUM, TOES, BALE
Down : DOME, PLUS, CUBE, TALK
Boxes : DUMP, LUCK, SOLE, BEAT
Note : Other anagrams of these words are OK as long as they don't change the answer grid.
Puzzle 422
The BrainBashers mechanical computer is a very sensitive device, it consists of interlocked toothed gear cogs.
The largest cog has 168 teeth and the others have 49, 32 and 15 respectively.
By accident, Daniel started to rotate the largest cog.
How many revolutions must he rotate the largest cog make before the computer is back in its starting position with all of the cogs where they started?
Hint: Try breaking each cog size into prime factors.
Answer: 140 revolutions.
If we break each wheel into its prime factors, we get:
168= 2 x 2 x 2 x 3 x 7
49 = 7 x 7
32 = 2 x 2 x 2 x 2 x 2
15 = 3 x 5
So
revolutions x 168

2 x 2 x 2 x 2 x 2 x 3 x 5 x 7 x 7
revolutions x 2 x 2 x 2 x 3 x 7

2 x 2 x 2 x 2 x 2 x 3 x 5 x 7 x 7
revolutions

2 x 2 x 5 x 7
revolutions

140
Which means revolutions = 140. QED.
Puzzle 423
Starting with the 6 in the bottom left corner, what is the highest total you can make, if you only move up or right, using the mathematical signs on the way?
A woman had three old coins  a silver dollar, a quarter, and a dime. Each coin was a little battered and had a piece missing. She found that exactly the same fraction had broken away from each coin.
What fraction of each was missing if the value of the remaining bits of coins was now exactly one dollar in total?
For this puzzle it can be assumed that ½ of a coin is worth ½ of its value.
[Ref: ZQJS] Based on a puzzle by Henry Ernest Dudeney.
Hint: A dollar is 100 cents, a quarter is 25 cents and a dime is 10 cents.
Answer: 7÷27 of each coin was missing.
The original value of the three coins was 100 + 25 + 10 = 135, and the new value was 100. So 35÷135 of the original value has been removed and 35÷135 = 7÷27. QED.
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