**Brain-teasing Riddles May 2017**

16th May 2017

Our riddles for you this month are a bit more wordy but no more or less challenging! We hope you enjoy them and that they are a welcome distraction from studying for those of our students who are currently sitting their exams. Do share with your friends and families - can you solve them all on your own first?

## Special Clock

Q: There is a clock that has an extra special way of telling the time. It does not have any hands or numbers whatsoever, but it has a chimer. If the time is 1 o'clock, it chimes once. If the time is 2 o'clock, it chimes twice, and so forth. The time gap between any two chimes is 2 seconds.

How many seconds would it take you to know the time, after the first chime is heard, if it is 10 o'clock?

A: If it is 10 o'clock, the clock will chime 9 times after the first chime is heard.

Since the time gap between any two chimes is 2 seconds, this will take 9 × 2 = 18 seconds.

However, this may seem pedantic but to know what time it really is you would actually have to wait an 'extra chime gap' to see if the clock chimes again. If you just dashed out of the door at 18 seconds there might be another chime you didn’t hear… So adding those extra 2 seconds, the total time required is 18 + 2 = 20 seconds.

## Which Digit?

Part 1. Q: Which digit is the most frequent between the numbers 1 and 1,000?

A: 1

So to figure out this you had to determine what distinguishes the number 1. We are including 1,000 which would be the first '1' in a new series of ten! So the digit 1 only has a single extra occurrence (301 occurrences) compared to 2 or 3 or 9 which have 300 occurrences each.

Part 2. Q: What digit is the least frequent between the numbers 1 and 1,000?

A: 0 is the least common digit even though 1,000 has three zero's !

The reason that zero has the least by far at only 192 occurrences is because zero does not have any equivalents to 22, 33, 44, 222, 3333 etc..

## The Vault

A robber got into a bank to rob its vault and noticed that the vault had an unusual lock. So he hid and watched how others got in. He noticed that the manager came up to the vault door and pressed a button. The lock read out a number in response to which the manager said a number of his own. On doing so the door opened.

This happened twice. The first time the lock said 12 and the manager responded with 6. Next the lock said 6 and the manager responded with 3. Believing that now he understood, the robber approached the door. The door said 10 so the robber entered 5. It set off the alarm and the robber went to prison.

What number should the robber have said?

A: The robber should have said 3 - the number of letters in the number the vault said which was 10

## Fortune Tellers

Q: You want to make a bet on an upcoming football match, and you have to choose between either Newcastle United or Manchester United. You come across a group of fortune telling machines who apparently can help you but each have varying rates of accuracy in their predictions.

The first machine has 75% chance of being correct. The second has 65% chance of being correct, the third 43%, the fourth 28%, and the fifth 10%. Which one do you choose?

A: The fifth fortune teller would allow you to get the best prediction of your future.

The fifth fortune teller predicts with only 10% accuracy. So, there is a 90% chance of the fifth fortune teller being wrong – whichever team they predict, you should bet on the opposite.

(Note: ConquerMaths does not condone or recommend gambling.)

## Big Family?

Q: Each child in a family has at least 2 brothers and 2 sisters. What is the smallest number of children the family might have?

A: If each boy in the family has at least 2 brothers, then the smallest number of boys is 3. Similarly, if each girl in the family has at least 2 sisters, then the smallest number of girls is 3.

So the smallest number of children the family might have is 6.

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