#2 Piles of money
Set by Katie Steckles
You are given a heap of N tokens, which you may divide into any number of smaller heaps. You will then receive an amount of money equal to the product of the number of tokens in each heap. The rules of this game state that if you were to just leave all the tokens in one heap, you would win 拢N.
What is the largest sum of money you can win starting with six tokens?
What about starting with 10 tokens?
Is there a general best strategy for N tokens?
Solution next week
#1 Digital sevens
Solution
106 is the next number after 95.
Two consecutive numbers would need to end in 9 and 0 to have their digit sum differ by 0 or a multiple of 7, and the smallest example is 69999, which has digits that add up to 42 (a multiple of 7), and 70000, which has a digit sum of 7.
For numbers two apart, the only pairs under 100 are (59, 61) and (68, 70).
Quick quiz #234
set by Bethan Ackerley
1 The condition in which certain sounds, such as chewing or a clock ticking, trigger negative emotional or physiological responses is known as what?
2 Who first discovered extraterrestrial radio waves?
3 What is the most abundant element in Earth's crust?
4 What was the first program deliberately designed to perform automated reasoning, subsequently described as the first artificial intelligence program?
5 Lentinan is a substance derived from which species of mushroom?
Quick quiz #234
Answers
1 Misophonia
2 Karl Jansky
3 Oxygen
4 Logic Theorist
5 The shiitake (Lentinula edodes)