Counting and multi-step puzzles · SET 9

How many different two-card hands can be made from the four cards shown? A hand is an unordered selection of two different cards.

Tom and Jerry start at the same point and walk in opposite directions at 5 and 7 miles per hour. How many miles apart are they after 4½ hours?

Two eight-sided dice are rolled. What is the probability that their sum is at least 12? AI reconstruction: both dice are fair, independent, and each is numbered 1 through 8.

The historical country outlines are drawn to the same scale. Which has the largest land area? Use the countries shown, including Yugoslavia and West Germany as they existed before 1990; do not replace West Germany with today’s reunified Germany. Diagram labels correspond to the options.

AI reconstruction. Added condition: count every square whose four sides are fully drawn, including larger squares that cross the borders between regions. Count only the blue diagram, not the alternative cards. How many squares are there? Enter the total as a number. The printed alternatives are retained below for reference and do not limit your answer.



Printed alternatives for comparison:

Which design is least like the other four?
AI reconstruction — added conditions: Compare whether the total number of closed square outlines is odd or even.

AI reconstruction: Treat AB and CD as the full major axes of two ideal Keplerian orbits about the same Sun; planet masses are negligible. CD is four times AB. If X takes one year to orbit, how long does Y take?

AI reconstruction. Each scale balances; equal shapes have equal values. What value balances the three blue circles?

Tokens are available only in values £8 and £5. What is the largest whole-pound total that cannot be made with a nonnegative whole number of these tokens? AI reconstruction: this restates the original casino-wager calculation as a token-sum puzzle; no change or borrowing is allowed.

Concrete has mass density 144 lb/ft³. Each rectangular paving slab is 3 ft × 2 ft × 2 in. How many COMPLETE slabs can be made from one ton? AI reconstruction: “ton” means a long ton of 2240 lb; use all material possible, with no waste. Original interval choices were A:9–11; B:11–13; C:13–15; D:15–17; E:17–19. Because intervals share endpoints, enter the whole-number count directly.

A shoe factory produces S pairs per hour. How many minutes does it take to make one pair? Assume S is positive and the production rate is constant.

Which labelled point represents the centre of gravity of this L-shaped plate? AI reconstruction: the metal has uniform density and thickness; dimensions are in one common unit. The outer width is 20, height 12, left-leg width 6 and top-bar height 4. Labels are schematic locations, not exact measuring marks.

The contents of one can weigh 1 pound 4 ounces. How many ounces do the contents of 24 cans weigh? Use 1 pound = 16 ounces.

Twenty soldiers have enough food for 45 days. Ten more soldiers arrive without food. At the same daily ration per person, how many days will the supplies feed all thirty?

AI reconstruction. Count the simple drawn components of the rocket and smoke. Count both circular contours of the porthole separately. Count the square as a square, not also a rectangle; do not count larger shapes made by combining components or regions caused by overlap. The four entries in each choice are triangles, circles, non-square rectangles and squares.

Mrs. Jones and her daughter Sally made 126 sandwiches for a church supper. Mrs. Jones made 6 more than twice as many as Sally. How many did Mrs. Jones make?

AI reconstruction: The written question was missing. The upper pair shows a transformation. Apply the same changes to the lower-left picture. Which option belongs in the lower-right box? Compare the shapes, positions, shading and directions.

An article is discounted by 50%. By what percent must its sale price increase to return to the original price?

AI reconstruction. The pictured scales balance. Identical shapes have identical values. Find the value of one green circle.

A 15-pound soil mixture contains 40% peat moss. The rest is sand and humus. How many pounds are sand and humus together?