To the Editor:

On June 12, I asked Albert Einstein of the Department for Advanced Study, and the Department of Mathematics, of Princeton University, to assist me with ascertaining the difficulty of solving, a certain mathematical problem--submitted herewith--and in partial remuneration for this favor, offered to pay to the person first to submit the correct solution within 30 days, the sum of $25.00; and a partial solution within the amount of 25,000 of the correct solution, $10.00; within the amount of 50,000, $5.00; and within the amount of 75,000, $1.00.

The failure of the Department for Advanced Study, the Department of Mathematics, and Albert Einstein either to solve or partly solve the problem presumably has established the fact that its solution and partial solutions are difficult; but not in what determinably exact degree difficult, and which, and with reasonable certainty, is my objective. For this objective can be reached only with a solution of the problem and a measurement of all measurable factors involved in the work of its solving. Therefore, as a further supplementation of the reward in exercise of the spirit of sportsmanship which efforts of solving the problem provide, for additional incentive, it is my desire to increase the offer of financial remunerations for a solution for a partial solution as follows; despite the fact that the problem now has been in the possession of the Department for Advanced Study, and available for study, for two months:

To the person first to submit the correct solution within 15 days--before September 28, 1941,--the sum of one hundred dollars ($100.00) will be paid: and a partial solution within the amount of 25,000 of the correct solution, fifty dollars ($50.00): within the amount of 50,000, twenty-five dollars ($25.00); within the amount of 75,000, fifteen dollars ($15.00); within the amount of 150.000 ten dollars ($10.00); within the amount of 500,000, five dollars ($5.00); and within the amount of 1,000,000, one dollar ($1.00): meaning that the partial solutions may be the above amounts, respectively, over or under the correct solution.

This--again--is the problem:

"Three times twelve tripled twelve times three tripled twenty-twos thrice, triple, twelve times, three thrice, tripled two twice tripled thirty-threes.

"Using one to three additional words, beginning with the letter 't', inserted within any three places next to each other, within the last twelve (for example, one, two or all three words, in one, two or all of the three places, being next to each other and within the last twelve, between the words 'two twice tripled thirty-threes')--thus making the problem contain from twenty-one to twenty-three words,--make the answer in the problem correct." C.A. Carlton,   6201 Kenwood Avenue,   Chicago, Illinois.