As Easy as 1,2,3
My calculator has 26 memories - one per letter of the alphabet. When I type a sequence of letters the calculator gives the product of all the numbers in the corresponding memories. I want to put numbers in the various stores so that when I type the word ONE it returns 1, and when I type the word TWO it returns 2, and when I type the word THREE it returns 3 and so on. How far can you get ? Is there an integer above which it is impossible to get ?
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Sum Equals Product
The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 � 1 [1/3]. What other numbers have the sum equal to the product and can this be so for any whole numbers?
Special Sums and Products
Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.