Every time you pick up a Martin Gardner book, there is still always a wonderful puzzle that one has not seen. This one is an original Martin Gardner puzzle, i.e. this is his own creation, published in the book The Colossal Book of Short Puzzles and Problems.
Please look at the figure above. This is a desk calendar made out of two cubes that Martin Gardner saw at the Grand Central station in New York in a shop. Each day from 01-31 can be indicated by the two cubes so that their front faces give the required date. Each face can have a unique digit from 0 through 9. What are the four digits that cannot be seen on the left cube and the three that cannot be seen on the right cube?
As always, please send your answers as comments within the blog (preferred), or send an e-mail to alokgoyal_2001@yahoo.com. Please do share the puzzle with others if you like, and please also send puzzles that you have come across that you think I can share in this blog.
Happy dating!
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Lets construct the solution.
The first cube should obviously have 0,1,2,3 and the second cube should have 1,2,3,4,5,6.
6 and 9 are mirror images.
So, we just have to take care of the dates 07, 08, 17, 18, 27, 28, 10, 20, 30
Note that 10,20,30 can be done by making second cube as first cube, and first cube as second cube.
Add 7 and 8 in the first cube. So make the first cube faces as 0,1,2,3,7,8.
17, 18, 27, 28 are also doable now.
For 07, 08 -> Just use the first cube in second slot and keep the first slot empty.
So the four digits that cannot be seen on the first block are 4,5,6,9 and the three that cannot be seen on the second block are 7,8,0.