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It's a Puzzlement

Card Trick
by John P. Robertson

Amy has seven cards numbered 1, 2, 3, 4, 5, 6, and 7. She randomly deals three each to Bill and Celia, keeping one for herself. All three people then look at their cards. Can Bill and Celia communicate with each other, in the presence of Amy, so that Bill and Celia can each determine what cards the other holds, but Amy will not know who holds any given card, other than the one that she herself holds?

Claims Data
Christopher Yaure's puzzle involved claim count data on five 12-month policies. He was supplied with claim counts on the five policies, and was subsequently provided with a corrected claim count for one policy. In the corrected claim count data, the mode was exactly the same as in the original data, the mean claim count was exactly 1 larger than the original data, the variance was exactly 2 larger, and the median was exactly 3 larger. Additionally, the final counts satisfied what Christopher called the "Rule of 3s":

The final number of claims for each policy was a multiple of 3.
The ratio of high to low number of claims was 3. Exactly 3 policies had an average of more than 3 claims per month.

The question was, what was the final claims frequency distribution?

A number of solvers determined that the final counts were 15, 36, 39, 45, and 45, and that the 39 had originally been reported as 34.

Solvers for this puzzle include Nicki C. Austin, Alan Erlebacher, Jon Evans, Sean Forbes, Moshe Goldberg, Betty-Jo Hill, John Hinton, Jim Mohl, Yipei Shen, David Uhland, Glenn Walker, and Mike Ziniti.

If you want to see how this solution can be derived, please e-mail me at JPR2718@AOL.COM.

Self-Referential Aptitude Test
In the last column, Sean Forbes should have been listed among the puzzle solvers.