Random Puzzles 

Workings

Hint
What do the fractions add up to?

Answer
There are 980 coins in the collection.

Reasoning
Using fractions:

   ¹/₂ + ¹/₄ + ¹/₅ = ¹⁹/₂₀

The remaining ¹/₂₀ is 49 coins.

Therefore, the ²⁰/₂₀ must equal 20 lots of 49 = 980.

Alternative Reasoning
Using percentages:

   50% + 25% + 20% = 95%

The remaining 5% is 49 coins.

If 5% is 49 coins, 10% is 98 coins, 100% is 980 coins.

Double-Checking
¹/₂ of 980 is 490
¹/₄ of 980 is 245
¹/₅ of 980 is 196
and the remaining 49 coins.

And 490 + 245 + 196 + 49 = 980.

Workings

Hint
One of the words starts and ends with T.

Answers
eve    = level able   = tablet carve  = scarves as     = ease, hash, sass on     = gong, sons ode    = codec, modem elude  = deluded ape    = lapel ate    = dated, rater rod    = erode

Workings

Hint
One of the words is clockwise.

Answers
foo + tpr + int = footprint
som + ewh + ere = somewhere
pin + eap + ple = pineapple
tec + hni + que = technique
ref + ere + nce = reference
pro + fes + sor = professor
bio + gra + phy = biography
clo + ckw + ise = clockwise
bar + ome + ter = barometer

Workings

Hint
You don't need to use a calculator.

Answer
Cube root of 2.

Reasoning
We could use a calculator to see that the tenth root of 10 = 1.2589 and the cube root of 2 = 1.2599.

But, if you've not got your calculator handy …

We have:

   10^1/10 or 2^1/3

Raise each to the power of 30 (since 10 x 3 = 30) to give:

   (10^1/10)³⁰ or (2^1/3)³⁰

   10^{1/10 x 30} or 2^{1/3 x 30}

   10³ or 2¹⁰

   1000 or 1024

Therefore, the cube root of 2 is larger.