Letter Equations 3 to 4

Hey, have any questions you'd like to see posted?  Send them along for others to try!

3 = W M.
3 = P C.
3 = W on a T.
3 = S on a S S.
3 = B M (S H T R).
3 = C in N A.
3 = N M in a L.

4 = H of the A.
4 = C V.
4 = Q in a G.
4 = I in a H.
4 = Y in the T of a P.
4 = B in a J.
4 = P in a B.
4 = F O in a G.
4 = S on a V.

PS, I'm on vacation this week, so the puzzle posting may be a little erratic.

Christmas Letter Equations

Merry Christmas and Happy Holidays!

8 = R in S S
0 = C S (not even a mouse!)


3 = T K of O are
12 = D of C


3 = G of C (P, P, and F)
4 = W in A 

8 = C on a M
4 = S to  a D

Do you know any other Christmas Letter Equations?  Post them in the comments below!

P.S.  I won't be posting a question tomorrow.

How Many Societies Just Give Tractors Away?

There are 3 societies A,B,C having some tractors each.

• A gives B and C as many tractors as they already have.
• After some days B gives A and C as many tractors as they have.
• After some days C gives A and B as many tractors as they have.
• Finally each has 24 tractors.

What is the original number of tractors each had in the beginning?

Submitted by Guess the Logo.

Letter Equations 0 to 2

0 = L in T.

1 = K E.
1 = C A in M.
1 = W on a U.
1 = H on a U.
1 = R A in E B.
1 = D at a T.
1 = G L for M.

2 = H in a W.
2 = B of C in a M.
2 = S of R in K R B.
2 = number it T to T.
2 = R on a T.
2 = S to an A.
2 = F of J.
2 = Q in a C.

Rare Years

Back in the year 1936, people born in 1892 were able to make an unusual mathematical boast, a boast that people born in 1980 will be able to make at some time during the 21st century. John Stuart Mill, the English philosopher and economist, would also have been able to make the same boast, had he noticed it.

Given that he was born in the 19th century, can you tell me what the unusual boast was, what year he was born in, and what year he could make the boast in?

Five and Six Letter Equations

I'm not sure I know the answers to these. Can you help me figure them out?

5 = F O in a G.
5 = S.
5 = R in the O F.
5 = G L.
5 = T on a F.
5 = L in a L.

6 = S on a G.
6 = P on a P T.
6 = P in an I H T.
6 = W of H the E.
6 = B C.

Count the

Fill in the blanks:

This sentence contains __ 1's, __ 2's, __ 3's, __ 4's, __ 5's, __ 6's, __ 7's, __ 8's, __ 9's and __ 0's.

There are two possible solutions. Try to find out both of them.

Even the Odds

Tim and Al are playing a game with two dice. They are not using numbers, but instead the die faces are colored. Some of the faces are colored blue and others are red.

Each player throws the dice in turn. Tim wins when the two top faces are the same color. Al wins when the colors are different. Their chances at winning are even.

The first die has 5 red faces and 1 blue face. How many red and how many blue are there on the second die?

US City

Which of the following anagrams is not a US city?

1. gronba
2. inhoxep
3. toditer
4. sangvelto
5. noterlam
6. dnartolp

Senior Play

In this year's Senior Class play, Ellis Island Idylls, a comedy celebrating America's ethnic heritage, Mike and four other boys play the five major male roles. Ironically, no one is playing the role for which he auditioned but instead is cast in one of the other four parts. Given this information and the clues, can you determine each actor's first and last name (one last name is Curtis), the part for which he auditioned, and the role he is playing in the production?

1. No two actors auditioned for and play the same two roles.
2. Tom is not the one playing Ivan.
3. Four of the actors - Ray, Evans, the one who tried out for Padraic, and the one portraying Ivan - had been in the Junior Class play.
4. The boy who auditioned for the role of Johann - who is not Pete Adams - is not playing Olaf in the production.
5. In one scene, Decker and the one who auditioned as Giorgio woo the same girl.
6. Ray did not try out as Ivan and did not win the Padraic role.
7. The boy who auditioned as Padraic - who is not Tom - is not the one playing Johann.
8. Steve and the Decker boy are also on the stage construction crew.
9. The actor playing Padraic auditioned as Olaf; he is not Tom.
10. The Block youth got the part for which Pete auditioned.

Are You Willing to Pay the Fine

Last Tuesday, five students majoring in literature - Judy, Lisa, Mary, Mike, and Phil - each received a notice from the university library for an overdue book (one book was by James Joyce). Can you determine each student's full name and the author of his or her overdue book?

1. After receiving the notices, three of the students returned their books on Wednesday: Mary, Ms. Snell, and the one who had the Ernest Hemingway novel.
2. Wicks and Jones (one of whom had the D.H. Lawrence novel) returned their books the same day.
3. Judy (who isn't Ames) isn't the one who had the William Faulkner novel.
4. Neither Mike (who didn't have the Faulkner novel) nor Wicks had ever been overdue at the library before.
5. Both Barr and the young woman who had the Joseph Conrad novel returned their books on Thursday.

Another Question About Alice

Another question submitted by Rich:

Alice is an ant that lives on a stick. Alice is no different from other ants : All ants walk at a speed of 1 metre per minute, are perpetually walking, and upon reaching the end of sticks or meeting other ants they turn and walk back the other way (they do not fall off nor can pass one another). We now place a finite number of ants on Alice's stick (again with Alice in the middle) and start them walking. We do not know how they are oriented. Could there be an ant in the middle of the stick after a minute? If so when would this ant be Alice?

I Just Like Saying Hyper Rooks

The following question was submitted by Rich (let me know if you want a link to somewhere?).

Consider an NxN chess board. What is the minimum number of Rooks (Castles) that it would take to dominate the board? Now consider an NxNxN hyper chess board. What is the minimum number of hyper rooks that it would take to dominate the board (NB Hyper Rooks can move up, down and across - ie in all 3 dimensions)?


The following image contains the answer as it was sent to me by Rich. I can't get the formulae to show in the comment section, so this is my best solution. So consider this a spoiler alert!

Watering the Scale

I've asked different versions of this question in the past, but I always find it interesting. How about you?

You have a glass of water sitting on a perfectly balanced scale. You put your finger into the glass and into the water. Your finger does not touch the glass, it only is submerged in the water. It makes the water go higher up the sides of the glass but it does not overflow.

What happens to the scale?

Who Done It?

Investigators break into an apartment and find the remains of 3 dead bodies on the floor in a pool of water. The only living occupant of the apartment was a cat in the corner.

The investigators quickly leave, never write up a report, investigate the dead bodies, or even send for an ambulance to pick them up.

What's going on here?

Do Not Pass This One

A woman pushing her car stopped outside a hotel and immediately went bankrupt. Explain.

Golfers Gaffe

Hogan and Snead are professional golfers and long-time rivals. One day during a game, they had each scored 30 when Hogan hit a bad shot. Snead immediately added 10 to his own score. Snead then hit a good shot and won the game. Why?

Easier Than Yesterday

• There are 8 balls.
• 7 balls are the same, the 8th is slightly heavier than the rest.
• You also have a balance-scale (the one with a platform on either side) but it has no markings on it.

Using the scale twice, locate the ball that is heavier.