Brain Teasers and Puzzles 

Workings

Hint
Start by looking at Clue 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.

Starting with Clue 2, we can place Ray, Emery, Logan and Riley as follows:

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

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

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

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

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

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

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

And Clue 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 Clue 3 and Clue 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
These are the first letters of the words: L, C, E, E, A, A, L, S, F, G, S, A, C, C, M.

Answer
---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 to?

Answer
There are 980 coins in the collection.

To check this we add:

 1÷2 + 1÷4 + 1÷5 + 49

this works out as

 490 + 245 + 196 + 49 = 980, as required.

To work the answer out from the question, we observe that:

1÷2 + 1÷4 + 1÷5 = 19÷20

and we know that there were 49 coins left, so 1÷20 of the collection is 49 coins.

This means that the entire collection is 20 x 49 = 980 coins.

Workings

Hint
How many minutes will the clock show for each real hour passed?

Answer
1.20pm.

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

The clock shows 10.12am, so we know that 612 clock minutes have passed.

Therefore, 612 ÷ 54 x 60 = 680 real minutes have passed, which is 11 hours and 20 minutes (11.20am).

The clock stopped 2 hours ago, therefore the time is now 1.20pm.