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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 407

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.

Using the BrainTracker grid below, how many words can you find? Each word must contain the central G and no letter can be used twice, however, the letters do not have to be connected. Proper nouns are not allowed, however, plurals are. Can you find the nine letter word?

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