Riddles and Brain Teasers

Suppose a small bank has one teller and customer transactions take 10 minutes on average. With 5.8 customers arriving per hour, what is the expected wait time? What would it be if you added a second teller?

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With one teller, customers will wait nearly five hours on average. But adding a second teller makes the wait go down to 3 minutes.Thanks to John D. Cook for this one.

With one teller, customers will wait nearly five hours on average. But adding a second teller makes the wait go down to 3 minutes.

Thanks to John D. Cook for this one.

Posted in Brain Teasers

The Average of Three

There are three numbers. The first two are 2/3 and 3/4.

What does the third number have to be to make the average of all three be 2?

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4 7/12In order for the average of three numbers to be 2, they must all add up to 6. That gives you this equation:
2/3 + 3/4 + n = 6Solve for n = 55/12, or 4 7/12.

4 7/12

In order for the average of three numbers to be 2, they must all add up to 6. That gives you this equation:
2/3 + 3/4 + n = 6

Solve for n = 55/12, or 4 7/12.

Posted in Brain Teasers

Alfred’s Tough Cash Request

Alfred is at the bank to cash his $200 check. He tells the cashier he would like some one dollar bills, ten times as many two dollar bills and the rest in fives.

How many of each denomination does the cashier need to give Alfred?

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Five $1 bills, 50 $2 bills and 19 $5 bills.We know that in order to give the rest of the amount in fives, the sum of the one and two dollar bills needs to be divisible by five (i.e. end in 0 or 5).If we start with a single one dollar bill, we’d need ten two dollar bills to satisfy the request, making $21. But we need a sum that is divisible by 5. So we keep going up, like so:$1 + $2 * 10 = $21
$2 + $2 * 20 = $42
$3 + $2 * 30 = $63
$4 + $2 * 40 = $84
$5 + $2 * 50 = $105 (Aha! It’s divisible by 5)
$6 + $2 * 60 = $126
$7 + $2 * 70 = $147
$8 + $2 * 80 = $168
$9 + $2 * 90 = $189So the only option that works is 5 $1 bills and 50 $2 bills, leaving $95 (95 / 5 = 19) to be paid out in 19 fives.Alfred is one tough customer.

Five $1 bills, 50 $2 bills and 19 $5 bills.

We know that in order to give the rest of the amount in fives, the sum of the one and two dollar bills needs to be divisible by five (i.e. end in 0 or 5).

If we start with a single one dollar bill, we’d need ten two dollar bills to satisfy the request, making $21. But we need a sum that is divisible by 5. So we keep going up, like so:

$1 + $2 * 10 = $21
$2 + $2 * 20 = $42
$3 + $2 * 30 = $63
$4 + $2 * 40 = $84
$5 + $2 * 50 = $105 (Aha! It’s divisible by 5)
$6 + $2 * 60 = $126
$7 + $2 * 70 = $147
$8 + $2 * 80 = $168
$9 + $2 * 90 = $189

So the only option that works is 5 $1 bills and 50 $2 bills, leaving $95 (95 / 5 = 19) to be paid out in 19 fives.

Alfred is one tough customer.

Posted in Brain Teasers

Aiden and Sofia Buying Candy

Aiden and Sofia were debating a major purchase of candy. They calculated that they could get three bags of jelly beans and two bags of chocolate for 24 cents, which was just under their limit of 25 cents. They found they could also get four bags of chocolate and two bags of jelly beans for the same 24 cents. How much did each bag of candy cost?

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Jelly beans are 6 cents and chocolate is 3 cents.

Posted in Brain Teasers