## Saturday, March 25, 2017

### 10-digit Number

Find a 10-digit number where the first digit is how many 0's there are in the number, the second digit is how many 1's in the number, the third digit is how many 2's, and so on, until the tenth digit which is how many 9's there are in the number.

Click below to see the answer.

## Saturday, March 18, 2017

### The Extra Dollar

Here is an old math puzzle that you can find many versions of online.

Two friends have a meal at a restaurant, and the bill is $25. The friends pay $15 each, which the waiter gives to the cashier. The cashier gives back $5 to the waiter. The friends tell the waiter to keeps $3 as a tip, so he hands back $1 to each of the two diners.

So, the friends paid $14 each for the meal, for a total of $28. The waiter kept $3, and that makes $31. Where did the extra dollar come from? Give yourself a moment to think about it before clicking below for the solution.

$25 is sitting with the cashier, $2 is back with the diners, and $3 is with the waiter. That adds to the required $30, so there really is no extra dollar.

The mistake is expecting that what the diners paid and what the waiter kept to add up to what they initially gave. Adding $28 and $3 is just a bit of sleight-of-hand. It's the amount that the meal effectively cost them (including tip), plus the amount they received back, that should add to $30.

The mistake is expecting that what the diners paid and what the waiter kept to add up to what they initially gave. Adding $28 and $3 is just a bit of sleight-of-hand. It's the amount that the meal effectively cost them (including tip), plus the amount they received back, that should add to $30.

Labels:
logic puzzles,
numbers

## Saturday, March 11, 2017

### Arranging Eights

Can you arrange eight 8's so that when added they will equal 1000? Click below to see the answer.

It's certainly possible to try all 22 different ways to partition eight identical digits, but there is a shortcut.

All of the numbers that are created by arranging eight 8's will end in the digit 8, and the sum of the last digits of those numbers must be a multiple of 10 (because the target sum of 1000 ends in 0), so we know there must be exactly five groups of digits in the correct solution. That means we only have to check 3 different partitions of the eight digits.

8888 + 8 + 8 + 8 + 8

888 + 88 + 8 + 8 + 8

88 + 88 + 88 + 8 + 8

These are the only three ways to partition eight identical objects into five groups, and they are the only groupings whose sums end in the digit 0. You can check with quick mental arithmetic that the second grouping is the correct solution.

All of the numbers that are created by arranging eight 8's will end in the digit 8, and the sum of the last digits of those numbers must be a multiple of 10 (because the target sum of 1000 ends in 0), so we know there must be exactly five groups of digits in the correct solution. That means we only have to check 3 different partitions of the eight digits.

8888 + 8 + 8 + 8 + 8

888 + 88 + 8 + 8 + 8

88 + 88 + 88 + 8 + 8

These are the only three ways to partition eight identical objects into five groups, and they are the only groupings whose sums end in the digit 0. You can check with quick mental arithmetic that the second grouping is the correct solution.

## Saturday, March 4, 2017

### A Unique Number

What is unique about the number 8,549,176,320? Click below to see the answer (and a bonus question).

There's nothing

*numerically*particularly unique or interesting about the number above. It is made up of all of the digits from 0 to 9, but a lot of numbers have that property. The unique thing about this number is that all of the digits from 0 to 9 are in alphabetical order when spelled out in English.**Bonus question:**Can you think of a number whose letters when spelled out in English are all in alphabetical order? Example: The first three letters of the word "five" are in alphabetical order, but the "e" at the end spoils it.
Labels:
brain teasers,
numbers,
puzzles

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