Matches

The man emptied a box of matches on the table and divided them into three heaps.

“You aren't going to start a bonfire, are you?” someone quipped.

“No, they're for my brain-teaser. Here you are – three uneven heaps. There are altogether 48 matches. I won't tell how many there are in each heap. Look well. If I take as many matches from the first heap as there are in the second and add them to the second, and then take as many from the second as there are in the third, and add them to the third, and finally take as many from the third as there are in the first and add them to the first – well, if I do all this, the heaps will all have the same number of matches.

How many were there originally in each heap?”

An Arithmatical Trick

“I'll give you an arithmatical trick and ask you to explain it. One of you – you, Professor, if you like – write down a three-digit number, but don't tell me what it is.”

“Can we have any noughts in it?”

“I set no reservations. You can wirte down any three numerals you want.”

“All right, I've done it. What next?”

“Write the same number alongside. Now you have a six-digit number.”

“Right.”

“Pass the slip to your neighbor, the one farther away from me, and let him divide this six-digit number by seven.”

“It's easy for you to say that, and what if it can't be done?”

“Don't worry, it can.”

“How can you be so sure when you haven't seen the number?”

“We'll talk after you've divided it.”

“You're right. It does divide.”

“Now pass the result to your neighbor, but don't tell me what it is. Let him divide it by 11.”

“Think you'll have your own way again?”

“Go ahead, divide it. There'll be no remainder.”

“You're right again. Now what?”

“Pass the result on and let the next man divide it, say, by 13.”

“That's a bad choice. There are very few numbers that are divisible by 13... You're certainly lucky, this one is!”

“Now give me the slip, but fold it so that I don't see the number.”

Without unfolding the slip, the man passed it on to the professor.
“Here is your number. Correct?”

“Absolutely.” The professor was surprised. “That is the number I wrote down.”

What Are the Digits?

Here is another similar problem.

In the following multiplication more than half of the digits are expressed by X’s.
The task is to find the missing digits.


  xx5
  1xx
  ---
 2xx5
13x0
xxx
-----
4x77x

Resolution of Digits

In the following multiplication more than half of the digits are expressed by X’s.


   x1x
   3x2
   ---
   x3x
 3x2x
x2x5
------
1x8x30

Can you restore the missing digits?

Thirty

The number 30 may easily be written by three 5’s:
5 X 5 + 5

It is harder to do it by using three other identical digits. Try it.

You may find several solutions.

Twenty-Four

It is very easy to write 24 by using three 8’s:
8 + 8 + 8

Can you do that by using three other identical digits?

There is more than one solution to this problem.

One Thousand

Can you write 1,000 by using eight identical digits (in addition to digits you may use signs of operation)?

About "Figures for Fun"

Figures for Fun is a book by Yakov Perelman.
It's a book of math puzzles, brainteasers, stories and conundrums.

It's a very old book (it was published in 1960's), and it is hard to find it at any bookstore now.

I will post some best puzzles here so that anyone who doesn't have access to this book can still enjoy it.