Numbers With the Same Product & Sum
A JavaScript web page for evaluating the sum and product of 4 numbers.
©2009, Bob Beeman
Updated 2009-09-30 @ 06:35 EDT (UT-4)
Read More
Important Notice

There is an old mathematical puzzle in which a customer goes to a 711 store and buys 4 items. The clerk says" "I multiplied the prices of your four items together, and you owe me $7.11."

The customer replies" "You are supposed to add the four prices, not multiply them!"

The clerk obliges the customer, then says: "I added the four prices and the total is still $7.11."

The question was: what are the four prices? The answer is shown below.

I am now posing another problem in which the four prices have Sum and Product equal to $20.09. The question is still: what are the four numbers?
Each of the four prices is a positive integer multiple of 0.01 (one cent) which could be individually paid in US currency.

There is a calculator below to help you. If you find the answer, EMAIL me from the link above. Good Luck!

Hide Value
Hide Value
Hide Value
Hide Value

Sum =
Product =

Read More
This page allows you to enter values for four variables and evaluate the sum and product of the values by clicking the "Calculate" button. The "Clear" button clears the four numbers and the Sum and Product fields.

When the page is first loaded (or re-loaded) it displays the answer to the now well-known "711" problem, where someone buys 4 items at 711 and the Sum and Product of the 4 prices are equal to $7.11.

Enter four other numbers to see if their Sum and Product are equal.

The "Hide Value" checkboxes, when checked, cause the associated number value to be hidden. This allows you to demonstrate that any particular 4 numbers DO actually have the properties claimed without revealing any more of them than you wish, although it does reveal the number of digits in the hidden ones.

Obviously, I have written software that discovers groups of four numbers with the property that their Sum and Product are equal. You will obtain this software from me when you pry it from my cold, dead hands (or hack my computer).

This page is copyrighted "freeware"
©2009, Bob Beeman
That means that although it is copyrighted, it is intended for you to use for education or entertainment. You may use it yourself, copy and redistribute it, or even put it on your own website. I ask only that you not make any changes. If you reuse any of the code, make sure to list me as one of your sources.

My only reward for writing this is the 15 milliseconds of fame I receive from having my name here. Don't deprive me of that.

You can copy this page by simply doing a "Save As" in your browser and putting it somewhere on your hard drive (or your web site). If you stop there the background will be gone. To preserve the background, copy the following file into this same folder, without changing its name, by again using your browser's "Save As". The next time you refresh the page, the background should be restored:


I make NO guarantee of any kind.
This page may contain serious errors.
Use this page entirely at your own risk!