I gave my niece and nephew the following puzzler:
A: Draw a 3x3 grid, with the boxes labeled 1 through 9 in the usual order (left to right; top to bottom).
B:For each of the following instructions you must write a number, greater than 10, starting in one box and going across (left to right) or down, with one digit to each box. Your answers should fill the grid, with no two answers overlapping.
C:Starting with a box whose number is a square, write a square number.
D:Starting with a box whose number is a cube, write a cube number.
E:Starting in a box whose number is prime, write a prime number whose digits add up to an even number.
F:Starting with a box whose number is even, write an even number
Unfortunately, one of the copies of my instructions had part F completely missing. Each child turned in a 3x3 grid which was correct for the version they had been given. By coincidence, they turned in identical grids.
How did they fill out their grids?
(In reply to Am I clueless?
The 1, 4 and 7 are in the leftmost column. You can only go right from there. In addition, the rules say you can only go from left to right, not right to left (or top to bottom, but not bottom to top).
So by your reasoning, you must go right from 1 (the cube), right from 4 (the square) and right from 7 (the prime) in the case of the response with clue F missing.
But the same digits in the same positions have to fit the 4-number version (including a number for clue F).
In the 4-clue way of looking at the grid, one number must be 3 digits long, and the other three 2 digits long (as each number must be greater than 10). It could be either vertical or horizontal, but not go through the center, so as not to separate the digits used for the 2-digit numbers into two sets of three. This will leave a 2x3 block to form the 2-digit numbers. They can all be parallel, or one on an end can be perpendicular to the other two.
Five formats fit for the 4-number way:
In each of these, the first two or three letters in SQUARE, CUBE, PRIME or EVEN are used to designate where the numbers go. Case and emphasis is used to help separate the abbreviations.
Vertical square *:
Horizontal cube (orig.):
Horizontal cube (orig.) *:
Horizontal square (orig. cube):
Edited on March 14, 2005, 7:07 pm
Posted by Charlie
on 2005-03-14 19:05:02