Brain Teasers and Puzzles 

Workings

Hint
Start by looking (2).

Answer
Ashley crossed first.

They crossed in the following order (first is on the right):

Alex, Sam, Quinn, Riley, Chris, Billie, Logan, Taylor, Emery, Jessie, Ray, Ashley.

Reasoning
Starting with (2), we can place Ray, Emery, Logan, and Riley as follows:

   Riley, -, -, Logan, -, Emery, -, Ray, -

(6) tells us that Taylor got on just after Emery, giving us:

   Riley, -, -, Logan, Taylor, Emery, -, Ray, -

(5) tells us that Jessie got on two people before Taylor, giving us:

   Riley, -, -, Logan, Taylor, Emery, Jessie, Ray, -

By (1), Chris got on two people after Logan, giving us:

   Riley, Chris, -, Logan, Taylor, Emery, Jessie, Ray, -

And (1) also tells us about Sam, giving:

   Sam, -, Riley, Chris, -, Logan, Taylor, Emery, Jessie, Ray, -

We now have a line of 11 people, the missing person is either in front of Ray, or behind Sam.

The only way to place Alex, Quinn, and Billie using (3) and (4) is if the missing person is behind Sam giving:

   -, Sam, -, Riley, Chris, -, Logan, Taylor, Emery, Jessie, Ray, -

And therefore we can now place Alex, Quinn, and Billie as follows:

   Alex, Sam, Quinn, Riley, Chris, Billie, Logan, Taylor, Emery, Jessie, Ray, -

But who crossed first?

The only person we've not yet found a space for is Ashley. So Ashley crossed first.

   Alex, Sam, Quinn, Riley, Chris, Billie, Logan, Taylor, Emery, Jessie, Ray, Ashley.

Workings

Hint
The first letters of the words are: L, C, E, E, A, A, L, S, F, G, S, A, C, C, M.

Answers
---rnt = learnt ---few = curfew ---ryo = embryo ---yme = enzyme ---rak = anorak ---urd = absurd ---ynx = larynx ---mpi = scampi ---hom = fathom ---ovy = groovy ---lpt = sculpt ---hma = asthma ---voy = convoy ---web = cobweb ---mur = murmur

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
How many clock minutes pass in a real hour?

Answer
1:20pm.

Reasoning
The clock now shows 10:12am, so we know that 10 x 60 + 12 = 612 clock minutes have passed.

Since the clock is losing 6 minutes every hour, for every real hour that has passed the clock will show 54 minutes.

So, 612 ÷ 54 ≈ 11.33 real hours have passed.

This equals 680 minutes, which is 11 hours and 20 minutes = 11:20am.

The clock stopped 2 hours ago, therefore the time must now be 1:20pm.