Can you solve it? Are you smarter than an English major?

Andrew Shore (Major-General Stanley) in The Pirates Of Penzance by Gilbert and Sullivan @ London Coliseum in 2015 Photograph: Tristram Kenton/The Guardian

With apologies to Gilbert and Sullivan, but I meant the other type of English major: a person who studied English at university.

American maths author Ben Orlin has a new book out aimed at this demographic. (More on this below.)

He suggested today’s puzzles – which are all solved with simple insights, the sort of thing that may appeal to mathematical novices.

For each question below, which option is bigger? No calculators allowed!

1. Square vs cube

• the sum of all squares from 1 to 100

• the sum of all cubes from 100 to 200

[Note: squares are the numbers 1², 2², 3², … and cubes are 1³, 2³, 3³, …]

[Update: there was a mistake in the original setting of this question. It’s now resolved.]

2. Sir Pentages

• 17% of 32

• 32% of 17

3. Fraction infraction

• 3997/4001

• 4996/5001

4. Roots shmoots

• the square root of 6

• the cube root of 15

5. Tick tock

• the number of seconds in a year,

• the number of hours in a millennium

6. Power shower

• 2¹⁰⁰

• 5⁴⁵

I’ll be back at 5pm UK with the solutions.

UPDATE: Solutions now up.

NO SPOILERS. Instead discuss your favourite English Majors.

Ben Orlin is a maths teacher from Minnesota known for Math with Bad Drawings, the name of a successful blog and a bestselling book full of charming, low-fi illustrations.

His new book Math for English Majors is a winning effort to convert people who don’t consider themselves ‘math-people’ to the joys of arithmetic, geometry, algebra and more.

Regular readers of this column may feel that some of today’s questions are a little easy. If so, you are probably not an English major – so please share with anyone who is!

Math for English Majors is out on September 26.

I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.

My new book, Think Twice: Solve the simple puzzles (almost) everyone gets wrong (Square Peg, £12.99), is out on September 5. To support the Guardian and Observer, order your copy at guardianbookshop.com. Delivery charges may apply.