X = Y in a Z (Part 1)

There have been a few of these types of puzzles on The Puzzle Page in the past, including: 12 I in a F, 12 N on the F of a C, and 3 F in a Y.  Here are a few more of the same type.

1. 9 P in the S S.
2. 1760 Y in a M.
3. 640 A in a S M.
4. 6.0221415×10²³ A in a M.
5. 52 C in a D of P C.
6. 206 B in the H B.

Simple Crypt-Addition

Here are four different arithmetic crypt problems for you to figure out. Each letter represents a different digit, and each problem is independent from each other problem. These are simple enough that you should be able to figure them out in your head, which means that they should also be great for introducing young puzzlers to cryptographic math puzzles.

   Y
   Y
 + Y
  MY
  

   XXX
 +   B
  BAAA
  

  ON
  ON
  ON
+ ON
  GO
  

  MA
 + A
  AM


For more puzzles like this get Brainteasers and Mindbenders by Ben Hamilton.

6 + 5 = 9?

In the image above are six lines.  Can you add five new lines, different from the six original lines, to end up with nine?

Thirds and Differences

Here's a nice little problem that can be figured out using algebra or using a little guess-work and a bit of luck.  It should be suitable for older elementary school or high school students.

1  2  3  4  5  6  7  8  9

Arrange the digits 1-9 so that the first 3 form a number that is 1/3 of the number formed by the last three and the three digits in the middle form a number that is the difference between them.

The numbers are as they appear, not summed.


There are 362880 ways to arrange the nine digits and 4 valid solutions to this puzzle.  Good luck!

Four Goes Into Eighteen

A reader asks:

"How do you create a sum of eighteen using four numbers repeating none of them?"

This one should be pretty simple, can you figure it out?

A Crossnumber Puzzle

Use the clues to fill in this crossnumber puzzle.

Clues
Across	Down
1. The cube of a whole number	1. A number that is unchanged if the digits are reversed
5. The number of square inches in a square yard	2. A prime number.
6. The number of cubic inches in a cubic foot.	3. The number of feet in a mile.
7. The number of millimeters in a meter.	4. The number of seconds in an hour.

A Different Kind of Sudoku

Here's a sudoku challenge of a slightly different sort. In the 5x5 grid shown below, write (x,y) pairs, with x and y ranging from 1 to 5 inclusively, with the stipulation that x and y values cannot be repeated in any row, column, or diagonal.

For instance, if you write the (x,y) pair (1,3) in the top left cell, then you can not have any other pairs with an x value of 1 or a y value of 3 in the top row, the left-most column, or the main diagonal that runs from the top left to the bottom right.

This puzzle can be solved fairly quickly and is not quite as difficult as it may seem.


Click on the picture for a larger version

7 and 7 and 7 and 7 is 56

Using four 7s and any of the basic arithmetic operators (+, -, x, ÷) can you make 56?


7    7    7    7 = 56

Taking Notes

If six boys can fill up six notebooks in six weeks and four girls can fill up four notebooks in four weeks, how many notebooks can a class of twelve boys and twelve girls fill up in twelve weeks?

Odd Arithmetic

Find four consecutive odd numbers that add up to 80.

Find five consecutive odd numbers that add up to 85.

The Red Herring

A 'Red Herring' is a plot device used in literature to distract the reader away from the main event of the story by focusing on a minor event or describing characters in ways that go against our sense of the way those character should be. In cryptography, a red herring is a second hidden message that is intended to be discovered more easily so that the real message remains hidden to anyone who might intercept the transmission and break the red herring code. Only the intended receiver would know the key to unlocking the real message.

The cryptogram below, with two hidden messages, is a prime example of a red herring. One message is fairly easy to decipher, especially if you were able to decode an earlier puzzle that appeared here: http://puzzlepage.blogspot.com/2008/01/find-hidden-message.html. The second message, the one that's the real message, is hidden using a different code that has been made to fit in the same grouping of numbers. This is an extremely difficult cryptogram to solve, so feel free to ask for hints in the comment section.


21941648698194164869819416486981
54961847952716486981947648697358
39114467658829115524463869851941
76487962174268859915413638294575
51947682873991174467835921746687
82992113426384971634855658399727
12432613829431624856389791172446
83953124636885997711344766849911
44758746436849618496184961849618
49361849618898184961849618496184
69819416486981941648698194164869
81961635248698194164869819416486
89915214466889912144668899114466
88279911446688995114466889911446
75879618496188921246648691144666
89921347658591134764869871924164
86921354456289291314419885991234
61839518465768533281559123134362
84931546687899361547678297124312
44951746678897194362778135951543
64856618399613949711429889811444
48896919466819961882828694114914
49981941698618994964219181649644


Good luck!

I Want Candy!

Donna bought one pound of jellybeans and two pounds of chocolate for $2. A week later, she bought four pounds of caramels and one pound of jellybeans, paying $3. The next week, she bought three pounds of licorice, one pound of jellybeans, and one pound of caramels for $1.50.

How much would she have to pay on her next trip if she bought a pound of each of the four kinds of candy?

It's Hip to be Square

Arrange two of each of the digits 0 through 9 to form a 20 digit number. The number may not begin with 0. Then score the number as follows:

For every two consecutive digits that form a perfect square, score two points. For every three consecutive digits that that form a perfect square, score three points. A four digit square scores four points, and so on.

For example, if your number was 58738219024719503664, you would get two points for 49, two points for 36, two points for 64, and six points for 219024 for a total of 12 points. You may not count 036 as a three digit square.

What is the maximum number you can score?

M & M

What comes next in the following sequence?

1212210202001, 224000000, 11333311, 623351, 290221, ...?

Who Gets Paid the Most?

Albert's weekly paycheck amounts to $250 plus 2/5 his weekly paycheck.

Charles' weekly paycheck amounts to $350 plus 3/5 his weekly paycheck.

Jane's weekly paycheck amounts to $450 plus 4/5 her weekly paycheck.

Susan's weekly paycheck amounts to $150 plus 1/5 her weekly paycheck.


How much does each person make in a week?

1 to 12 in a Cross

Write the numbers 1 through 12 in the squares below so that the two columns, the two rows, and the five squares that can be formed with four numbers in each have a total sum of 26.


Can you find the solution where no two consecutive numbers are next to each other horizontally, vertically, or diagonally?

1 to 19 in a Honeycomb

Can you place the numbers 1 through 19 in the honeycomb shown below so that there is a difference of at least 4 between any adjacent cells?

Seven Pairs of Numbers

If two 1s, two 2s and two 3s are arranged like this:

2 3 1 2 1 3

then the two 1s enclose 1 other digit, the two 2s enclose 2 other digits, and the two 3s enclose 3 other digits.


Can you find a similar arrangement using the seven pairs 1, 1, 2, 2,...7, 7?

A Sequence of Numbers

Professor Egghead showed one of his graduate students the following 3 numbers:

1 5 9

and asked him "Do you know what the next one is?"

The student replied, "With only three numbers it would be very difficult to figure out the sequence but it appears to be an arithmetic series with each number being 4 more than the previous one."

Professor Egghead smiled knowingly and said "Some say the fourth number of the sequence is 3 times the second number, others claim it is the sum of the first three. Do you know the fifth, which is also the last number of the series?"

The student wrote four numbers on a piece of paper and was totally baffled as to what the last number could be. "Why would you think I should know this?" he asked.

Professor Egghead answered "Because you like to read."