More Hand Shadows by H. Bursill

By H. Bursill

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The frog climbs upward 5 feet in the daytime. During the night, it goes to sleep and slips back 4 feet. At this rate, how many days will it take the frog to get out of the well? How did you arrive at your answer? 48. A teacher has 24 students in her class. She divides the students into three groups, II in the first, 7 in the second, and 6 in the third, in order that she can work individually with each of the separated groups. However, she later decides that all groups must have an equal number of students, or 8 in each group.

Two can play, and no trick is involved in winning this game. The game follows the pattern of tic-tac-toe; one player, at his turn, use~ any of the odd digits, 1, 3, 5, 7, 9, and the other uses even digits, 2, 4, 6, 8. The one using the odd digits has an extra one and always goes first. The player who can make a straight row - vertically, horizontally or diagonally - add to the sum of 15 first wins. Naturally, each player tries to keep the other from scoring. Example: A has 1,3, 5, 7,9. B has 2, 4, 6, 8.

The corridors on the ends count as being in two different corridors, as the diagram shows. The guard did not bother to note the number of men in each individual jail, as sometimes the men would stay in a neighboring cell instead of their own, but always within the same side or corridor. So, on some occasions, there might be 11 men in one cell and only 7 in another as 2 men switched cells. But the guard was always careful to see that there were a total of 27 men on each side or corridor. One day the prisoners managed to get an extra set of keys which would open all 8 cells.

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