Roberta’s old calculator keeps only one digit after the decimal point, discarding later digits after EVERY operation. Thus 7/5 gives 1.4 exactly, but 7/4 gives 1.7 instead of 1.75, an error of 0.05. For (7/4)/2 it first gets 1.7, then 0.8 instead of 0.875, an error of 0.075. What is the error when it calculates ((10/3)*(10/3))*9?
A beaver and its friends connect to the internet through the cable along the pictured poles. A single cable break has disconnected the internet.
A command such as ping 2001:db8::ff00:42:8329 tests a computer’s connection: a reply such as “64 bytes from ... time=22.9m” means it is reachable, while “100% packet loss, time 999ms” means a break lies between it and the starting pole. The beaver wants to use as few ping commands as possible. What is the minimum number needed to guarantee locating the broken link?
In the beavers’ team ball game, a shot over the crossbar is a point worth 1 and a shot below it is a goal worth 3.
The score g-p means g goals and p points:1-2 gives 5, 0-2 gives 2, 2-0 gives 6. Scores 1-5 and 2-2 both give 8, a draw. Four games finish as follows: game 1 Lyreen River Beavers 1-3, Rye River Beavers 2-1; game 2 Lyreen 2-1, Rye 0-4; game 3 Lyreen 1-6, Rye 2-4; game 4 Lyreen 1-2, Rye 0-5. How many games are draws?
At 10 am Bob leaves his house to reach a friend in Beaver Town for dinner at 9 pm, at most 11 hours later. He must buy a gift at Beaver Market and collect his son Rob at Beaver School before reaching Town. His remaining fuel permits 4 hours of driving; after refueling at Gas Station he can drive 9 more hours. Road labels give hours.
Which printed routes meet these requirements? Place-name translations in the options abbreviate Beaver Bob’s House, Beaverlake, Beaver Mountains, Gas Station, Beaver Tower, Beaver Forest, Beaver School, Beaver Market and Beaver Town. Select all valid options.
House → Lake → Gas → Tower → Forest → School → Forest → Market → Town
House → Mountains → Tower → Market → Forest → School → Town
House → Lake → Gas → Tower → Market → Forest → School → Town
House → Lake → Gas → Tower → Forest → School → Forest → Town
A substitution rule rewrites one letter as a string. For example A→BB and B→ABA give A→BB→ABAABA→BBABABBBBABABB after three simultaneous steps: every letter is replaced at each step. Which listed rule set can produce BAACCACCABAB?
The famous blue diamond has been stolen and replaced by a green fake.
Exactly 2000 visitors entered its room one at a time, in a known order. Inspector Bebro asks selected visitors whether the diamond they saw was blue or green. Everyone answers truthfully except the thief, who says green. He wants to identify the thief with as few interviews as possible. Which promise can he truthfully make?
I can guarantee finding the thief by interviewing fewer than 20 people.
20 interviews are insufficient unless lucky, but fewer than 200 always suffice.
At least 200 and at most 1999 interviews are necessary.
There is no guarantee; in the worst case every visitor must be interviewed.
Leslie transports logs through canals from S to T in one day, earning one beaver dollar per delivered log. Each directed arrow has a daily log capacity. Logs move only along arrow directions; four intermediate stations lie between S and T.
What is the largest number of logs deliverable in one day?
An electronic noticeboard program uses + to join quoted text strings. Although + can mean numerical addition, inside quoted text it is an ordinary displayed character. For example “10:47” + “ ” + “BEAVER FALLS” + “ - ” + “PLATFORM” + “ ” + “3” displays “10:47 BEAVER FALLS - PLATFORM 3”. What does “7 + 8” + “ + ” + “1 + ” + “2” + “5” display?
Beavers repaint a 16 m×16 m museum floor using numbered plan sheets that refer to one another. Each sheet gives its scale; the first illustration shows how a 10 m sheet uses two 5 m detail sheets.
The actual recursive plan below refers to itself. One beaver says the second sheet is essential because it tells them when to stop.
The left sheet applies at 16 m, 8 m, …, 1 m; the second, solid-gray diagram applies at 0.5 m. Preserve the orientation of each reference number when placing a smaller copy. Which floor pattern results?
A central leafy tree is surrounded by two bare trees and two palms.
A monkey takes 3 seconds between the center and any other tree, 2 seconds between a bare tree and a palm in either direction, and 7 seconds between the two bare trees or the two palms. The five trees have different labels P, Q, R, S, T. The monkey visits P, Q, S, R, T, R, P in that order. Which labels can occupy the center if the total travel time is as small as possible?
Alonzo’s computer uses prefix expressions: (max x 1…xn) is the largest input, (min x 1…xn) the smallest, (+ x 1…xn) their sum, and (* x 1…xn) their product. They may be nested: (+ (* 2 3) (+ 1 2)) equals 9. Evaluate (+ (max (min 3 9 2) (* (min 0 4) (max 0 4))) (min (max 3 6) (max 5 7 2))).
A programmable bee has four commands: move forward one square, turn left 90° without moving, turn right 90° without moving, and move backward one square.
GO executes the stored program. The example presses left, forward, right, forward, left, GO and shows its resulting movement.
The program is remembered, so pressing GO again repeats it from the current state. If the program brings the bee back to its starting square, what is the largest number of GO presses needed to return to that square with exactly its original direction?
In this fictional diagram puzzle, a bomb must be defused by selecting and cutting both wires of one module. Each module has an LED(on or off), two wires with pictured colors/patterns, and a lining color.
There are six modules. Odd-position modules share certain properties; even-position modules share other properties. Choose the module that has both sets of shared properties.
