Math Is Fun Forum

Show that any integer that is not a power of 2 can be written as the
sum of consecutive integers.

A,B,C, can do a work in 8,14,16 days respectively. A does the work for 2 days. B continues from it and finishes till 25% of the remaining work. C finishes the remaining work. How many days would have taken to complete the work

In the diagram below, there are six glasses in a row. The first three are full and the second three are empty. By moving only one glass, arrange the six glasses so that the glasses alternate: full, empty, full, empty, full, empty.

solve the cryptarithm

What are the positive integers x for which

solve in R

If
x∈ [-5,4]

then x² ∈ [.......,....]

and 1/x ∈ .........

If

(a) x<y        ( B)  x> y        (C)x=y          (D)noon of these

A lecture hall has 24 lamps.

Each lamp may operate 4 light bulbs at most.

When the maintenance staff has installed four bulbs in some of the lamps, it became clear that the number of bulbs available was not enough. Then they continued with three bulbs per lamp,

then two bulbs per lamp,

and finished the job with one bulb per lamp. How many bulbs were missing if there were twice as many lamps with one bulb as with four bulbs, and there remained no bulbs at all for half as many lamps as those with three bulbs?