Puzzles, Mazes and Numbers by Charles Snape

By Charles Snape

This booklet comprises lots of the fabric from How confusing, How outstanding and the way many? via a similar authors. It includes attention-grabbing information regarding numbers and mazes, either ancient and smooth, with lots of puzzles, difficulties and investigational actions. there are answers and tricks to a couple of the issues on the finish of the publication.

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The Powers That Be You may have wondered why a number raised to the zero power is one. You may have thought that a number raised to the zero power should be itself (because the number is not multiplied by anything, so it should just remain itself ). But then you probably then remembered that a number raised to the first power is itself, and you would not want a number raised to the power 0 to equal the same number as the number raised to the power 1. But why couldn’t we have a number raised to the power 0 be 0, just as a number multiplied by 0 is 0?

Etc. Now, draw a diagonal line, beginning with the first digit of the first number, the second digit of the second number, the third digit of the third number, ad infinitum. The unending diagonal number we get will begin 7074553 . . Add 1 to each digit of our diagonal number. The new number will begin 8185664 . . Notice that the diagonal number we end up with cannot be the same as the first number because its first digit is an 8, not a 7. It cannot be the same as the second number because its second digit is a 7, not a 6.

The largest has over 130,000 digits. All are even numbers. Is there an odd perfect number? No one has discovered one or proven that there could not be one. Incidentally, a “sublime” number is one that has the number of divisors (that leave no remainder) that is perfect and the sum of these divisors is perfect. There are only two known sublime numbers. One is 698, 655,567,023,837,898,670,371,734,243,169,822,657,830,773,351,885,970, 528,324,860,512,791,691,264. The other is 12 (1 + 2 + 3 + 4 + 6 + 12, the six divisors, sum to 28).

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