Can you solve it? Tasty buns for Easter eggheads

Today’s paschal problems are from the archive of US puzzle maker Sam Loyd [1841-1911]. Two dynamo teasers for ‘dynamo teaser’*.

1. The famous hot cross bun puzzle

This familiar nursery rhyme conceals a riddle:

Hot cross buns, hot cross buns,
One a penny, two a penny,
Hot cross buns.
If you have no daughters
Give them to your sons!
Two a penny, three a penny,
Hot cross buns.
I had as many daughters
As I had sons.
So I gave them seven pennies
To buy their hot cross buns.

In other words, hot cross buns come in three kinds: those sold at one a penny, two a penny and three a penny. I have an equal number of boys and girls. My children spend exactly seven pennies on buns.

The puzzle is asking that if every child gets the same number and kinds of buns, how many buns, and of what kinds, does each child receive? (Assume that the buns remain whole.)

2. A study in eggs.

How many eggs can you put in a 6×6 crate such that no row, column, or diagonal has more than two eggs in it? The first two have already been placed, in opposing corners, as shown above. Can you draw me their positions?

Hint: the answer is more than 10 (including the two already in the crate).

Sam Loyd was the US’s preeminent puzzle ‘entrepreneur’: in the late 19th century he invented, adapted, illustrated and popularised a huge number of puzzles, which appeared in many newspapers, magazines, advertisements and books. He was perhaps the first person to realise that you could make a living from writing mathematical puzzles.

PLEASE NO SPOILERS. I’ll be back at 5pm UK with the answers.

*It’s an anagram.

I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.

I’m the author of several books of puzzles, most recently the Language Lover’s Puzzle Book.

Two compendiums – Mathematical Puzzles of Sam Loyd, and More Mathematical Puzzles of Sam Loyd – both edited by Martin Gardner, are published by Dover Publications. They contain reprints from Sam Loyd’s Cyclopedia of Puzzles, published in 1914.