## February 2013 Logic & Maths Puzzles

1. TOY STORY

Three friends talked about Ivan The Inventor, but only one of them knew the truth about him.

“Ivan has invented hundred of toys”, Gerry said.

“No he hasn’t”, George said. “He has invented fewer than that”

“Well, he has invented at least one toy”, Anita said.

If only one of those three statements is true, can you work out how many toys Ivan has actually invented?

2. At a recent visit to the reptile house at a local zoo, I counted a total of 27 heads and 70 feet. I was counting snakes, lizards and people. There were twice as many lizards as there were people.

(a) How many snakes were there?

(b) How many lizards were there?

(c) How many people were there?

3. A porter leads five guests to their hotel rooms, rooms 1 to 5.

Unfortunately the keys are unlabelled and the porter has mixed up the order.

Using trial and error, what is the maximum number of attempts the porter must make before he opens all the doors?

4. PICK-UP STICKS

The diagram represents nine sticks in a pile, coloured (in no particular order) red, green, yellow, blue, orange, brown, grey, purple and pink. In what order would you remove all the sticks consecutively, lifting stick by stick, so as not to disturb lower sticks?

5. PENTAHEXES

A pentahex is a shape formed by joining five regular hexagons.

The honeycomb on the left has been made by assembling eleven pentahexes.

To make it easier, each pentahex in the honeycomb has been outlined with a black boundary.

Which three of the four pentahexes, a, b, c and d have been used in making up the honeycomb? (They can be rotated to fit)

6. TETRAHEDRON

A tetrahedron or regular triangular pyramid is shown. Two faces (red and green) are shown, and the other two faces (blue and yellow) are hidden.

The tetrahedron is then viewed from the four different directions shown by the arrows.

Which view (a, b, c, d or e) is NOT possible?

7. As Miss Nozemoke entered the interview room, her host told her to keep eye contact with Mr. Lighter, since he would be the one making the final decision in her case. “However,” he continued, “the men routinely change positions, but I can give you some clues that you can use to figure out who is sitting where.” Miss Nozemoke mentally numbered the men 1 to 4 from left to right and used the clues to work out where Mr. Lighter sat.

Where did Mr. Lighter sit? (Position 1,2,3 or 4?)

Clues:

•The pipe smoker will sit to the right of Mr. Lighter.

•Mr. Crumpet does not smoke cigarettes.

•Neither Mr. Crumpet nor Mr. Tray will sit in the third position.

•The cigarette smoker will sit to the immediate left of Mr. Small.

•Mr. Crumpet will not smoke cigars.

•The cigarette smoker is just to the right of the cigar smoker.

•The cigar smoker is sitting on the end.

8. Three brothers, Alan, Brian and Chuck are all different ages. They each do strange things with numbers, that is, instead of saying the actual number, they change it in a certain way first.

• One brother divides the number in half.

• Another brother squares the number.

• The third brother reverses the digits. (21 becomes 12, 50 and also 5 become 5)

When they were asked their ages, the oldest whispered his “age” to the thinnest, who whispered it to Chuck, who whispered it to the youngest, who answered: 27.

Then the youngest whispered his “age” to the tallest, who whispered it to Brian, who whispered it to the shortest, who answered: 23

Lastly, the youngest whispered his “age” to the shortest, who whispered it to the thinnest, who whispered it to Alan, who answered: 16.

What are the ages of the three brothers?

9. How many times do the hour and the minute hands of a clock cross each other in any twelve-hour period?

10. VEGETABLE NUMEROLOGY

Assign every letter of the alphabet a number so that A=1, B=2, C=3 and so on. The word CAB would then be worth 3 + 1 + 2 = 6

Now arrange these vegetables from lowest score to highest;

carrot, cabbage, leek, pea

SOLUTIONS