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
There are no larger squares than size 4 x 4.

Answer
There are 110 squares without a rook.

Reasoning
There are 60 squares of size 1 x 1.
There are 35 squares of size 2 x 2.
There are 12 squares of size 3 x 3.
There are  3 squares of size 4 x 4.

Giving a total of 60 + 35 + 12 + 3 = 110 squares.

Workings

Hint
Think of an alternative alphabet.

Answer
N.

From epsiloN, last letters of the Greek alphabet, alpha, beta, gamma, delta, epsilon, zeta, eta, theta, iota, kappa, lambda, mu.

Workings

Hint
How many boxes of toys can 1 toy maker make in 5 hours?

Answer
Five toy makers.

Reasoning
How many boxes of toys can 1 toy maker make in 5 hours?
2 toy makers can make 6 boxes of toys in 3 hours
1 toy maker  can make 3 boxes of toys in 3 hours
1 toy maker  can make 1 box   of toys in 1 hour
1 toy maker  can make 5 boxes of toys in 5 hours

So 4 toy makers could only make 20 boxes of toy in 5 hours, and we require the extra toy maker to make the remaining 2 boxes of toys.