Understanding Powers of 2 Problem

Understanding Powers of 2 Problem

Assessment

Interactive Video

Mathematics

10th - 12th Grade

Hard

CCSS
4.OA.C.5, 7.NS.A.2B, 7.NS.A.3

+1

Standards-aligned

Created by

Olivia Brooks

FREE Resource

Standards-aligned

CCSS.4.OA.C.5
,
CCSS.7.NS.A.2B
,
CCSS.7.NS.A.3
CCSS.7.NS.A.2A
,
The video discusses a mathematical problem involving selecting integers such that the sums of pairs are powers of 2. The challenge is to find distinct numbers that maximize these sums. The problem is introduced with examples using two and three numbers, leading to an open question about four numbers. Stan Wagon's historical problem is explored, and Rob Pratt's approach using linear programming is discussed. The video concludes with an exploration of solutions for five numbers and thoughts on the problem's complexity.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main challenge in the 'Powers of 2' problem?

Finding four numbers whose pair sums are all powers of 2

Finding numbers that are all powers of 2

Finding any two numbers whose sum is a power of 2

Finding three numbers whose sum is a power of 2

Tags

CCSS.4.OA.C.5

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why can't the numbers 1, 1, 1, 1 be used in the problem?

They do not sum to a power of 2

They are not integers

They are all negative

They are not distinct

Tags

CCSS.4.OA.C.5

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the best solution for three numbers to achieve powers of 2?

-1, 3, 5

1, 3, 5

1, 2, 5

2, 4, 6

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the conjecture regarding four numbers in the problem?

It is only possible with positive numbers

It is solved with four numbers

It is possible but not proven

It is impossible to find four numbers

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Who is associated with the problem discussed in the video?

Neil deGrasse Tyson

Albert Einstein

Stan Wagon

Rob Pratt

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What programming technique did Rob Pratt use to approach the problem?

Neural networks

Genetic algorithms

Mixed integer linear programming

Dynamic programming

Tags

CCSS.7.NS.A.2B

CCSS.7.NS.A.2A

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What assumption did Rob Pratt make to solve the problem?

Numbers are all even

Numbers are all negative

Numbers are within a certain range

Numbers are all positive

Tags

CCSS.7.NS.A.3

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