4. How many changes can be given to seven notes of a piano? That is to say, in how many ways can seven keys be struck in succession, so that there shall be some difference in the order of the notes each time?

5. At a time when eggs were scarce, an old woman who possessed some good hens, wishing to oblige her friends, sent her daughter with a basket of eggs to three of them; at the first house, which was the squire’s, she left half the number of eggs she had, and half a one over; at the second she left half of what remained and half an egg over; and at the third she again left half of the remainder, and half a one over; she carried home one egg in her basket, not having broken any. How many had she when she started?

6. Two drovers, A and B, meeting on the road, began discoursing about the number of sheep they each had. Says B to A, “Pray give me one of your sheep and I will have as many as you.” “Nay,” replied A, “but give me one of your sheep and I will have as many again as you.” Required to know the number of sheep they each had?

7. To tell at what hour a person intends to rise. Let the person set the hand of the dial of a watch at any hour he pleases, and tell you what that hour is; and to the number of that hour you add in your mind twelve; then tell him to count privately the number of that amount upon the dial, beginning with the next hour to that on which he proposes to rise, and counting backwards, first reckoning the number of the hour at which he has placed the hand. How is it done?

“The Two Travelers.”

8.Two travelers trudged along the road together,
Talking, as Yankees do, about the weather;
When, lo! beside their path the foremost spies
Three casks, and loud exclaims, “A prize, a prize!”
One large, two small, but all of various size.
This way and that they gazed, and all around,
Each wondering if an owner might be found.
But not a soul was there—the coast was clear—
So to the barrels they at once drew near;
And both agree, whatever may be there,
In friendly partnership they’ll fairly share.
Two they found empty, but the other full,
And straightway from his pocket one doth pull
A large clasp-knife; a heavy stone lay handy,
And thus in time they found their prize was brandy.
’Tis tasted and approved; their lips they smack,
And each pronounces ’tis the famous Cognac.
“Wont we have many a jolly night, my boy?
May no ill luck our present hopes destroy!”
’Twas fortunate one knew the mathematics,
And had a smattering of hydrostatics;
Then measured he the casks, and said, “I see
This is eight gallons—those are five, and three.”
The question then was how they might divide
The brandy, so that each should be supplied
With just four gallons, neither less nor more,
With eight, and five and three, they puzzle sore;
Filled up the five, filled up the three, in vain.
At length a happy thought came o’er the brain
Of one; ’twas done, and each went home content,
And their good dames declared ’twas excellent.
With those three casks they made division true;
I found the puzzle out; say, friend, can you?
9.“To five and five and fifty-five
The first of letters add;
It is a thing that pleased a king,
And made a wise man mad.”
10.“The sum of four figures in value will be
Above seven thousand nine hundred and three;
But when they are halved you’ll find, very fair,
The sum will be nothing, in truth, I declare.”

ANSWERS TO CONUNDRUMS.