An incomplete pairwise balanced design is equivalent to a pairwise balanced design with a distinguished block, viewed as a ‘hole’. If there are v points, a hole of size $w$ , and all (other) block sizes equal $k$ , this is denoted $\text{IPBD}\left( \left( v;w \right),\,k \right)$ . In addition to congruence restrictions on $v$ and $w$ , there is also a necessary inequality: $v\,>\,\left( k\,-\,1 \right)w$ . This article establishes two main existence results for $\text{IPBD}\left( \left( v;w \right),\,k \right)$ : one in which $w$ is fixed and $v$ is large, and the other in the case $v>\,\left( k-1+\varepsilon \right)w$ when $w$ is large (depending on $\varepsilon$ ). Several possible generalizations of the problemare also discussed.

We distribute the points and lines of PG(2, 2n+1) according to a special structure that we call the daisy structure. This distribution is intimately related to a special block design which turns out to be isomorphic to PG(n, 2).

We show a blocking set of 3q points in PG(2, 2n+1)that intersects each line in at least two points and we apply this to find a lower bound for the heterochromatic number of the projective plane.

This study describes two experiments undertaken to explore the clinical significance and cognitive substrates of Block Design broken configurations in children. Broken configurations were defined as instances in which the child placed a block outside the 2 × 2 or 3 × 3 square matrix. In Experiment 1, 336 normal children between the ages of 6 and 14 were administered WISC–III Block Design. Broken configurations were fairly common, but almost always self-corrected. The tendency to break configurations was inversely related to overall Block Design performance and mother's level of education, and directly related to the perceptual cohesiveness of the design. In Experiment 2, children were administered WISC–III Block Design and a global–local similarity judgment task. The frequency of broken configurations was inversely related to global perceptual bias. Taken together, the results of these experiments indicate that while broken configurations are common, particularly on designs with high perceptual cohesiveness, a high number of broken configurations or final answers containing broken configuration are associated with weaker visuospatial skills. Broken configurations are also made more frequently by children whose perception is less influenced by the global properties of spatial stimuli. (JINS, 1999, 5, 518–524.)